Robert Harley

In the paper:

  "The Distribution of Small Gaps Between Successive Primes",
  Mathematics of Computation, volume 28, number 125, January 1974.

Richard P. Brent, described how to compute approximate counts of prime gaps using Hardy and Littlewood's conjecture. The slowest part is computing an integer function T_{r,k}, 1 <= k <= r, which takes him O(2^(2r/3)) operations. Using a slightly different algorithm with a run-time something like O(2^(2r/ln(r))), I computed these values up to r = 70. Here is a table of the non-zero values in case you have a use for these numbers!

T_{ 1, 1} = 1
      
T_{ 2, 1} = 1
      
T_{ 3, 1} = 2
T_{ 3, 2} = 2
      
T_{ 4, 1} = 3
T_{ 4, 2} = 4
T_{ 4, 3} = 1
      
T_{ 5, 1} = 4
T_{ 5, 2} = 6
T_{ 5, 3} = 2
      
T_{ 6, 1} = 30
T_{ 6, 2} = 56
T_{ 6, 3} = 30
T_{ 6, 4} = 4
      
T_{ 7, 1} = 18
T_{ 7, 2} = 40
T_{ 7, 3} = 28
T_{ 7, 4} = 6
      
T_{ 8, 1} = 15
T_{ 8, 2} = 40
T_{ 8, 3} = 36
T_{ 8, 4} = 12
T_{ 8, 5} = 1
      
T_{ 9, 1} = 30
T_{ 9, 2} = 92
T_{ 9, 3} = 100
T_{ 9, 4} = 44
T_{ 9, 5} = 6
      
T_{10, 1} = 180
T_{10, 2} = 624
T_{10, 3} = 812
T_{10, 4} = 480
T_{10, 5} = 120
T_{10, 6} = 8
      
T_{11, 1} = 150
T_{11, 2} = 504
T_{11, 3} = 632
T_{11, 4} = 350
T_{11, 5} = 72
      
T_{12, 1} = 2970
T_{12, 2} = 10880
T_{12, 3} = 15642
T_{12, 4} = 11008
T_{12, 5} = 3780
T_{12, 6} = 504
      
T_{13, 1} = 1620
T_{13, 2} = 6688
T_{13, 3} = 11090
T_{13, 4} = 9378
T_{13, 5} = 4224
T_{13, 6} = 952
T_{13, 7} = 84
      
T_{14, 1} = 1782
T_{14, 2} = 7400
T_{14, 3} = 12312
T_{14, 4} = 10400
T_{14, 5} = 4634
T_{14, 6} = 1008
T_{14, 7} = 80
      
T_{15, 1} = 3960
T_{15, 2} = 19312
T_{15, 3} = 38958
T_{15, 4} = 41768
T_{15, 5} = 25376
T_{15, 6} = 8570
T_{15, 7} = 1446
T_{15, 8} = 90
      
T_{16, 1} = 22275
T_{16, 2} = 113792
T_{16, 3} = 244829
T_{16, 4} = 287904
T_{16, 5} = 200805
T_{16, 6} = 84280
T_{16, 7} = 20583
T_{16, 8} = 2656
T_{16, 9} = 140
      
T_{17, 1} = 23760
T_{17, 2} = 122400
T_{17, 3} = 265734
T_{17, 4} = 315120
T_{17, 5} = 220944
T_{17, 6} = 92466
T_{17, 7} = 22120
T_{17, 8} = 2700
T_{17, 9} = 128
      
T_{18, 1} = 757350
T_{18, 2} = 3979008
T_{18, 3} = 8883060
T_{18, 4} = 10966172
T_{18, 5} = 8160360
T_{18, 6} = 3743544
T_{18, 7} = 1040798
T_{18, 8} = 166040
T_{18, 9} = 13644
T_{18,10} = 448
      
T_{19, 1} = 400950
T_{19, 2} = 2239104
T_{19, 3} = 5333232
T_{19, 4} = 7045200
T_{19, 5} = 5612012
T_{19, 6} = 2737436
T_{19, 7} = 788592
T_{19, 8} = 120186
T_{19, 9} = 7140
      
T_{20, 1} = 504900
T_{20, 2} = 2915840
T_{20, 3} = 7236810
T_{20, 4} = 10062640
T_{20, 5} = 8559382
T_{20, 6} = 4558512
T_{20, 7} = 1490236
T_{20, 8} = 279200
T_{20, 9} = 25632
T_{20,10} = 768
      
T_{21, 1} = 908820
T_{21, 2} = 5777920
T_{21, 3} = 16006998
T_{21, 4} = 25293628
T_{21, 5} = 25040302
T_{21, 6} = 16042408
T_{21, 7} = 6621546
T_{21, 8} = 1691666
T_{21, 9} = 243872
T_{21,10} = 16210
T_{21,11} = 294
      
T_{22, 1} = 8835750
T_{22, 2} = 56689920
T_{22, 3} = 159615504
T_{22, 4} = 258927336
T_{22, 5} = 267006488
T_{22, 6} = 182041376
T_{22, 7} = 82606080
T_{22, 8} = 24436076
T_{22, 9} = 4458038
T_{22,10} = 445104
T_{22,11} = 17952
      
T_{23, 1} = 8330850
T_{23, 2} = 55372800
T_{23, 3} = 161805900
T_{23, 4} = 272787560
T_{23, 5} = 292530312
T_{23, 6} = 207276852
T_{23, 7} = 97483328
T_{23, 8} = 29693850
T_{23, 9} = 5502392
T_{23,10} = 541736
T_{23,11} = 20016
      
T_{24, 1} = 15904350
T_{24, 2} = 110218240
T_{24, 3} = 337714368
T_{24, 4} = 601500212
T_{24, 5} = 688462352
T_{24, 6} = 528267460
T_{24, 7} = 274911048
T_{24, 8} = 95882496
T_{24, 9} = 21589178
T_{24,10} = 2909644
T_{24,11} = 201728
T_{24,12} = 4972
      
T_{25, 1} = 10602900
T_{25, 2} = 78453760
T_{25, 3} = 259208326
T_{25, 4} = 503845272
T_{25, 5} = 638819850
T_{25, 6} = 553348174
T_{25, 7} = 333200948
T_{25, 8} = 139061136
T_{25, 9} = 39323050
T_{25,10} = 7178822
T_{25,11} = 771934
T_{25,12} = 40444
T_{25,13} = 600
      
T_{26, 1} = 8675100
T_{26, 2} = 65815552
T_{26, 3} = 222480280
T_{26, 4} = 441115188
T_{26, 5} = 568043690
T_{26, 6} = 496665190
T_{26, 7} = 299126614
T_{26, 8} = 123115352
T_{26, 9} = 33552948
T_{26,10} = 5667978
T_{26,11} = 519164
T_{26,12} = 18536
      
T_{27, 1} = 15904350
T_{27, 2} = 125480960
T_{27, 3} = 445109722
T_{27, 4} = 936691472
T_{27, 5} = 1299110200
T_{27, 6} = 1247084166
T_{27, 7} = 846351674
T_{27, 8} = 407142718
T_{27, 9} = 136899012
T_{27,10} = 31105922
T_{27,11} = 4478894
T_{27,12} = 360574
T_{27,13} = 11960
      
T_{28, 1} = 257650470
T_{28, 2} = 2057036800
T_{28, 3} = 7401008550
T_{28, 4} = 15847906176
T_{28, 5} = 22467234164
T_{28, 6} = 22193313780
T_{28, 7} = 15655667118
T_{28, 8} = 7952068360
T_{28, 9} = 2895713696
T_{28,10} = 743552820
T_{28,11} = 130445250
T_{28,12} = 14782880
T_{28,13} = 969120
T_{28,14} = 27552
      
T_{29, 1} = 222660900
T_{29, 2} = 1776107520
T_{29, 3} = 6375729282
T_{29, 4} = 13593395200
T_{29, 5} = 19128593472
T_{29, 6} = 18668443948
T_{29, 7} = 12918700344
T_{29, 8} = 6366803478
T_{29, 9} = 2211452320
T_{29,10} = 527416896
T_{29,11} = 82484676
T_{29,12} = 7844956
T_{29,13} = 399104
T_{29,14} = 8100
      
T_{30, 1} = 16604141400
T_{30, 2} = 137449159680
T_{30, 3} = 514590231096
T_{30, 4} = 1151172876672
T_{30, 5} = 1712427905900
T_{30, 6} = 1783275849600
T_{30, 7} = 1332662130802
T_{30, 8} = 720521099012
T_{30, 9} = 280433370000
T_{30,10} = 77181262520
T_{30,11} = 14532377696
T_{30,12} = 1774107900
T_{30,13} = 128975226
T_{30,14} = 4843936
T_{30,15} = 67200
      
T_{31, 1} = 6441261750
T_{31, 2} = 56911196160
T_{31, 3} = 228830896980
T_{31, 4} = 553838648256
T_{31, 5} = 899233690940
T_{31, 6} = 1033124953150
T_{31, 7} = 863141800752
T_{31, 8} = 530478526848
T_{31, 9} = 239751903028
T_{31,10} = 78777761916
T_{31,11} = 18369533720
T_{31,12} = 2915154534
T_{31,13} = 293137524
T_{31,14} = 16351382
T_{31,15} = 367552
      
T_{32, 1} = 6226553025
T_{32, 2} = 54069370880
T_{32, 3} = 213249174660
T_{32, 4} = 505037201552
T_{32, 5} = 799957727050
T_{32, 6} = 893157886368
T_{32, 7} = 721531916562
T_{32, 8} = 425908066056
T_{32, 9} = 183169043337
T_{32,10} = 56517842560
T_{32,11} = 12135950902
T_{32,12} = 1721143800
T_{32,13} = 147584208
T_{32,14} = 6550848
T_{32,15} = 112320
      
T_{33, 1} = 13836784500
T_{33, 2} = 127085826560
T_{33, 3} = 532897145178
T_{33, 4} = 1350034178880
T_{33, 5} = 2304270553388
T_{33, 6} = 2797174955788
T_{33, 7} = 2484362101368
T_{33, 8} = 1635525293974
T_{33, 9} = 799505921412
T_{33,10} = 287863227268
T_{33,11} = 74936047534
T_{33,12} = 13668343964
T_{33,13} = 1663472704
T_{33,14} = 125284200
T_{33,15} = 5175900
T_{33,16} = 91350
      
T_{34, 1} = 6641656560
T_{34, 2} = 63757824000
T_{34, 3} = 280475561070
T_{34, 4} = 748667274256
T_{34, 5} = 1353200542126
T_{34, 6} = 1749907156172
T_{34, 7} = 1667427651782
T_{34, 8} = 1187717946838
T_{34, 9} = 634711470646
T_{34,10} = 253000600276
T_{34,11} = 74055977086
T_{34,12} = 15480295878
T_{34,13} = 2207599238
T_{34,14} = 199031808
T_{34,15} = 9862880
T_{34,16} = 192160
      
T_{35, 1} = 9962484840
T_{35, 2} = 96876953600
T_{35, 3} = 432135635850
T_{35, 4} = 1171099054240
T_{35, 5} = 2152382571534
T_{35, 6} = 2835785493016
T_{35, 7} = 2759909244350
T_{35, 8} = 2014530552238
T_{35, 9} = 1108039672762
T_{35,10} = 457350869200
T_{35,11} = 139837955468
T_{35,12} = 30944771326
T_{35,13} = 4778251840
T_{35,14} = 487520528
T_{35,15} = 30442852
T_{35,16} = 1064164
T_{35,17} = 18816
      
T_{36, 1} = 435858711750
T_{36, 2} = 4341200912384
T_{36, 3} = 19890493216704
T_{36, 4} = 55548398353920
T_{36, 5} = 105609934037258
T_{36, 6} = 144585042777240
T_{36, 7} = 147013719890738
T_{36, 8} = 112853773847024
T_{36, 9} = 65818149695190
T_{36,10} = 29109653091480
T_{36,11} = 9668529195900
T_{36,12} = 2367339177312
T_{36,13} = 414768995340
T_{36,14} = 49670750140
T_{36,15} = 3784555236
T_{36,16} = 162368120
T_{36,17} = 2979504
      
T_{37, 1} = 224155908900
T_{37, 2} = 2258481971200
T_{37, 3} = 10485155702790
T_{37, 4} = 29727848617632
T_{37, 5} = 57509346598784
T_{37, 6} = 80322576915068
T_{37, 7} = 83574029162340
T_{37, 8} = 65878208525724
T_{37, 9} = 39608684408832
T_{37,10} = 18136932095412
T_{37,11} = 6264191334804
T_{37,12} = 1600844158000
T_{37,13} = 293085317616
T_{37,14} = 36456896856
T_{37,15} = 2811462016
T_{37,16} = 112121310
T_{37,17} = 1405120
      
T_{38, 1} = 230748729750
T_{38, 2} = 2411472967680
T_{38, 3} = 11646227156256
T_{38, 4} = 34464227113728
T_{38, 5} = 69858296785638
T_{38, 6} = 102699532806420
T_{38, 7} = 113090240638294
T_{38, 8} = 94980077296328
T_{38, 9} = 61362749906514
T_{38,10} = 30530722672060
T_{38,11} = 11633891012650
T_{38,12} = 3353415754800
T_{38,13} = 716559419004
T_{38,14} = 110184341212
T_{38,15} = 11696423466
T_{38,16} = 810181320
T_{38,17} = 33751448
T_{38,18} = 689472
      
T_{39, 1} = 475482231000
T_{39, 2} = 5056905641984
T_{39, 3} = 24879391641270
T_{39, 4} = 75091338143520
T_{39, 5} = 155456237650394
T_{39, 6} = 233797081544148
T_{39, 7} = 263891934090706
T_{39, 8} = 227713534939218
T_{39, 9} = 151586934803914
T_{39,10} = 77985040623608
T_{39,11} = 30856603351642
T_{39,12} = 9281105407498
T_{39,13} = 2080266780954
T_{39,14} = 336823629344
T_{39,15} = 37538402896
T_{39,16} = 2661185116
T_{39,17} = 103715324
T_{39,18} = 1553664
      
T_{40, 1} = 11332326505500
T_{40, 2} = 122267833425920
T_{40, 3} = 611333513121420
T_{40, 4} = 1878969903287040
T_{40, 5} = 3970507565362870
T_{40, 6} = 6111795030108760
T_{40, 7} = 7083406761250116
T_{40, 8} = 6300241614515392
T_{40, 9} = 4343194458469710
T_{40,10} = 2327366695151460
T_{40,11} = 966415973394924
T_{40,12} = 308155698303488
T_{40,13} = 74292815006406
T_{40,14} = 13234573074528
T_{40,15} = 1687552260700
T_{40,16} = 147779920800
T_{40,17} = 8452964462
T_{40,18} = 295737904
T_{40,19} = 5189184
      
T_{41, 1} = 8717174235000
T_{41, 2} = 95681838120960
T_{41, 3} = 487113052565106
T_{41, 4} = 1525850855944192
T_{41, 5} = 3289438770811056
T_{41, 6} = 5171436235308420
T_{41, 7} = 6128844426141488
T_{41, 8} = 5581656225549888
T_{41, 9} = 3945575974799680
T_{41,10} = 2171379563508894
T_{41,11} = 927506301661440
T_{41,12} = 304733719269234
T_{41,13} = 75810269580360
T_{41,14} = 13946598106740
T_{41,15} = 1834787555380
T_{41,16} = 164967003550
T_{41,17} = 9574497744
T_{41,18} = 335025360
T_{41,19} = 5989984
      
T_{42, 1} = 836325696105900
T_{42, 2} = 9215602937856000
T_{42, 3} = 47202334156525626
T_{42, 4} = 149142658039276032
T_{42, 5} = 325308110778037958
T_{42, 6} = 519344911076101632
T_{42, 7} = 627785341613387860
T_{42, 8} = 586297034625286456
T_{42, 9} = 427822125718108110
T_{42,10} = 245064585020029120
T_{42,11} = 110108539956614750
T_{42,12} = 38575457625997800
T_{42,13} = 10420691735978092
T_{42,14} = 2134292368550048
T_{42,15} = 323911898837298
T_{42,16} = 35410728853240
T_{42,17} = 2707729336050
T_{42,18} = 141690118032
T_{42,19} = 4919614808
T_{42,20} = 90478080
      
T_{43, 1} = 356968284923250
T_{43, 2} = 4072898572288000
T_{43, 3} = 21633731461881000
T_{43, 4} = 71005296100137984
T_{43, 5} = 161183359278762180
T_{43, 6} = 268368111134480008
T_{43, 7} = 339128859159088416
T_{43, 8} = 331982345586920210
T_{43, 9} = 254699894371280936
T_{43,10} = 153929109487740906
T_{43,11} = 73255234405634944
T_{43,12} = 27301794662074920
T_{43,13} = 7881540452637900
T_{43,14} = 1732002769340138
T_{43,15} = 282440262314448
T_{43,16} = 32954135285214
T_{43,17} = 2611402346748
T_{43,18} = 130185778650
T_{43,19} = 3594920208
T_{43,20} = 39744000
      
T_{44, 1} = 387187822271250
T_{44, 2} = 4463881633792000
T_{44, 3} = 23980004976526326
T_{44, 4} = 79682286267592704
T_{44, 5} = 183337657035704452
T_{44, 6} = 309817175019838848
T_{44, 7} = 397975852337067900
T_{44, 8} = 396744615775804984
T_{44, 9} = 310638281093588580
T_{44,10} = 192078091670055360
T_{44,11} = 93809745627849172
T_{44,12} = 36012562653889860
T_{44,13} = 10756775161928664
T_{44,14} = 2459325567403600
T_{44,15} = 420017369979996
T_{44,16} = 51713879906052
T_{44,17} = 4355828888200
T_{44,18} = 231451257312
T_{44,19} = 6743643240
T_{44,20} = 77907060
      
T_{45, 1} = 929250773451000
T_{45, 2} = 11103863001907200
T_{45, 3} = 61990862057937216
T_{45, 4} = 214714768952209920
T_{45, 5} = 516705475463371688
T_{45, 6} = 916762024826645872
T_{45, 7} = 1241878510848564212
T_{45, 8} = 1312251497360173406
T_{45, 9} = 1095557303258607490
T_{45,10} = 727454698640349046
T_{45,11} = 384794778177376044
T_{45,12} = 161673354562318272
T_{45,13} = 53553420048545308
T_{45,14} = 13811411868027004
T_{45,15} = 2722369321597070
T_{45,16} = 399596251105906
T_{45,17} = 42156863760386
T_{45,18} = 3049822524742
T_{45,19} = 142329327510
T_{45,20} = 3904669788
T_{45,21} = 47393280
      
T_{46, 1} = 16427826173508750
T_{46, 2} = 197897755259043840
T_{46, 3} = 1115566808193836100
T_{46, 4} = 3908546274171474432
T_{46, 5} = 9534346700737182536
T_{46, 6} = 17189440096131216000
T_{46, 7} = 23729902481023782108
T_{46, 8} = 25641498571177720592
T_{46, 9} = 21982779628726399054
T_{46,10} = 15066039779773700976
T_{46,11} = 8278396738311457730
T_{46,12} = 3642645596328287196
T_{46,13} = 1277112672978031956
T_{46,14} = 353567459687065728
T_{46,15} = 76266393723264360
T_{46,16} = 12583737949418760
T_{46,17} = 1549807086234598
T_{46,18} = 137932847428096
T_{46,19} = 8469158055984
T_{46,20} = 329063525076
T_{46,21} = 6277128000
      
T_{47, 1} = 16029575842029750
T_{47, 2} = 195779421831168000
T_{47, 3} = 1120457650667669028
T_{47, 4} = 3991788817584733184
T_{47, 5} = 9919300906421185944
T_{47, 6} = 18255879107466773040
T_{47, 7} = 25790168494984542000
T_{47, 8} = 28600222742606378136
T_{47, 9} = 25249269222627530564
T_{47,10} = 17891422331281694028
T_{47,11} = 10212480732408720480
T_{47,12} = 4694427777622581670
T_{47,13} = 1730875198672866820
T_{47,14} = 507905788106783286
T_{47,15} = 117187939674022080
T_{47,16} = 20899315425847768
T_{47,17} = 2814864559039080
T_{47,18} = 277703714986434
T_{47,19} = 19289475752904
T_{47,20} = 894595077540
T_{47,21} = 25225225168
T_{47,22} = 322560000
      
T_{48, 1} = 31362213603971250
T_{48, 2} = 390603330971238400
T_{48, 3} = 2281569526378818990
T_{48, 4} = 8304439726783567872
T_{48, 5} = 21106895683478405972
T_{48, 6} = 39784878897063956288
T_{48, 7} = 57651231507074162846
T_{48, 8} = 65698299730393550706
T_{48, 9} = 59733752404638457140
T_{48,10} = 43710156171765100334
T_{48,11} = 25854030412569009884
T_{48,12} = 12370262181918895310
T_{48,13} = 4775882375226905970
T_{48,14} = 1479545686404101018
T_{48,15} = 364608354978947098
T_{48,16} = 70626699392871458
T_{48,17} = 10589803178839244
T_{48,18} = 1205593025527458
T_{48,19} = 101585531894986
T_{48,20} = 6080541341184
T_{48,21} = 236137037892
T_{48,22} = 4536301100
      
T_{49, 1} = 18817328162382750
T_{49, 2} = 240180048396288000
T_{49, 3} = 1439357594534951364
T_{49, 4} = 5381358541502828544
T_{49, 5} = 14066734732797946074
T_{49, 6} = 27304983980097161728
T_{49, 7} = 40801738006023714396
T_{49, 8} = 48015204986631081624
T_{49, 9} = 45145311850510119292
T_{49,10} = 34209049141837962568
T_{49,11} = 20979580831996603478
T_{49,12} = 10417947402745994070
T_{49,13} = 4176190677559491992
T_{49,14} = 1342524240747948450
T_{49,15} = 342458374352027652
T_{49,16} = 68257074785732032
T_{49,17} = 10402283276165848
T_{49,18} = 1175675730676662
T_{49,19} = 94261569774990
T_{49,20} = 5000891056854
T_{49,21} = 154605823776
T_{49,22} = 2022271080
      
T_{50, 1} = 20908142402647500
T_{50, 2} = 269986905010995200
T_{50, 3} = 1637925447477541482
T_{50, 4} = 6203859307904275968
T_{50, 5} = 16443770980946288916
T_{50, 6} = 32401875186240467648
T_{50, 7} = 49218000545241169758
T_{50, 8} = 58977867831770861780
T_{50, 9} = 56589514043998565718
T_{50,10} = 43882786680849458778
T_{50,11} = 27641586217377023832
T_{50,12} = 14166137706398208960
T_{50,13} = 5898728359864927632
T_{50,14} = 1987218426812417014
T_{50,15} = 537817605465074254
T_{50,16} = 115756389393901674
T_{50,17} = 19551140647847750
T_{50,18} = 2547429044512502
T_{50,19} = 250575776107190
T_{50,20} = 18082691967140
T_{50,21} = 916246161856
T_{50,22} = 29805089200
T_{50,23} = 478800000
      
T_{51, 1} = 33453027844236000
T_{51, 2} = 445992030175232000
T_{51, 3} = 2797323861604767588
T_{51, 4} = 10969670320547582080
T_{51, 5} = 30147240680953267488
T_{51, 6} = 61682962852777161376
T_{51, 7} = 97429493462536287676
T_{51, 8} = 121566831391720214630
T_{51, 9} = 121602354476728926416
T_{51,10} = 98397260065096563882
T_{51,11} = 64706038485115531190
T_{51,12} = 34612336471090121472
T_{51,13} = 15023176039766205832
T_{51,14} = 5259623091476247292
T_{51,15} = 1470858230270363544
T_{51,16} = 323898918458896000
T_{51,17} = 55054809577972878
T_{51,18} = 7026751741702566
T_{51,19} = 648144944833228
T_{51,20} = 40921090915446
T_{51,21} = 1630237838468
T_{51,22} = 35721801064
T_{51,23} = 316207500
      
T_{52, 1} = 872439760255927500
T_{52, 2} = 11632659954499584000
T_{52, 3} = 73068616724919602220
T_{52, 4} = 287392918609130176512
T_{52, 5} = 793536177242952081796
T_{52, 6} = 1634403918694196276288
T_{52, 7} = 2604398734096932221280
T_{52, 8} = 3286454942375587944720
T_{52, 9} = 3333993205511058400240
T_{52,10} = 2744674306085698486416
T_{52,11} = 1842858121401838635330
T_{52,12} = 1010573291118666109040
T_{52,13} = 451695596224836978456
T_{52,14} = 163660627297781384104
T_{52,15} = 47619191412471208494
T_{52,16} = 10969647055244087976
T_{52,17} = 1959911559859794730
T_{52,18} = 263626974680454624
T_{52,19} = 25545137701540512
T_{52,20} = 1664525185210624
T_{52,21} = 64791369328218
T_{52,22} = 1177572548400
T_{52,23} = 4046544000
      
T_{53, 1} = 815417553703252500
T_{53, 2} = 10998467421221683200
T_{53, 3} = 69905601477741961350
T_{53, 4} = 278299667147111409408
T_{53, 5} = 778026968530043837952
T_{53, 6} = 1623014143056568613728
T_{53, 7} = 2620332419380620047900
T_{53, 8} = 3351350682999245322720
T_{53, 9} = 3447164997480115098000
T_{53,10} = 2878442304835702363384
T_{53,11} = 1961061997045801746684
T_{53,12} = 1091587523777858203682
T_{53,13} = 495424251880652905520
T_{53,14} = 182327394788403868848
T_{53,15} = 53899642514570903340
T_{53,16} = 12618353073414143422
T_{53,17} = 2291832037931727168
T_{53,18} = 313561705291512440
T_{53,19} = 30954088076371872
T_{53,20} = 2065329111857022
T_{53,21} = 83862457719744
T_{53,22} = 1731144105936
T_{53,23} = 13357512000
      
T_{54, 1} = 1599472893802533750
T_{54, 2} = 21991649479819264000
T_{54, 3} = 142626523034655502866
T_{54, 4} = 580036631545341333504
T_{54, 5} = 1658652301960146737362
T_{54, 6} = 3544494182017953412560
T_{54, 7} = 5872536115528820726710
T_{54, 8} = 7723875038089850364912
T_{54, 9} = 8190561778382114339450
T_{54,10} = 7072420294899642019162
T_{54,11} = 5001306191380748104878
T_{54,12} = 2902990141588202769510
T_{54,13} = 1381931186093641374998
T_{54,14} = 537397608663995799112
T_{54,15} = 169474880995519061222
T_{54,16} = 42857145631135857734
T_{54,17} = 8549758257882457376
T_{54,18} = 1314527806529199470
T_{54,19} = 150608278059260714
T_{54,20} = 12226724160736744
T_{54,21} = 648869444000454
T_{54,22} = 19462831229776
T_{54,23} = 234627886704
      
T_{55, 1} = 1184794736150025000
T_{55, 2} = 16859671669800960000
T_{55, 3} = 113402284046134888374
T_{55, 4} = 479392457805790470144
T_{55, 5} = 1428494592766413777574
T_{55, 6} = 3189625825866809747296
T_{55, 7} = 5538154844652822968774
T_{55, 8} = 7658726745848271141284
T_{55, 9} = 8570498175790734960094
T_{55,10} = 7841767030108829207254
T_{55,11} = 5903388996261958758904
T_{55,12} = 3667314316625188105690
T_{55,13} = 1880008791392177707080
T_{55,14} = 793072342272734288602
T_{55,15} = 273708728311875469998
T_{55,16} = 76575512538913594328
T_{55,17} = 17135473474146656486
T_{55,18} = 3009387016149433986
T_{55,19} = 403835051230427806
T_{55,20} = 39837681078866066
T_{55,21} = 2726178673625610
T_{55,22} = 117941760127526
T_{55,23} = 2736937010836
T_{55,24} = 23930334360
      
T_{56, 1} = 959683736281520250
T_{56, 2} = 13712728208506880000
T_{56, 3} = 92587655462342220342
T_{56, 4} = 392749937183022833664
T_{56, 5} = 1173814675779951688186
T_{56, 6} = 2627350921554179201408
T_{56, 7} = 4569972355364292790198
T_{56, 8} = 6326005067393790776552
T_{56, 9} = 7079248026479175420208
T_{56,10} = 6469936935675976587804
T_{56,11} = 4858273685108037737078
T_{56,12} = 3005227223951082261618
T_{56,13} = 1530802080720006934418
T_{56,14} = 639968956219274996508
T_{56,15} = 218163185152633476740
T_{56,16} = 60032562455056615200
T_{56,17} = 13140006983713488160
T_{56,18} = 2240666170044945346
T_{56,19} = 289006999279481600
T_{56,20} = 27012221271226360
T_{56,21} = 1714524808651300
T_{56,22} = 66591102390988
T_{56,23} = 1322469364568
T_{56,24} = 9684057600
      
T_{57, 1} = 1693559534614447500
T_{57, 2} = 24820686660231168000
T_{57, 3} = 172249764562704048258
T_{57, 4} = 752738537844280452096
T_{57, 5} = 2323706006675990642724
T_{57, 6} = 5387995536387560638664
T_{57, 7} = 9740675971910079247190
T_{57, 8} = 14067034929046878452412
T_{57, 9} = 16493578453177235470190
T_{57,10} = 15871158019053011191528
T_{57,11} = 12618891715031282053286
T_{57,12} = 8319415048829092336976
T_{57,13} = 4551431985429323602396
T_{57,14} = 2062345333600700896100
T_{57,15} = 770411166270122757832
T_{57,16} = 235449677832936957046
T_{57,17} = 58204791944419087480
T_{57,18} = 11452679709729558144
T_{57,19} = 1753354574235875870
T_{57,20} = 202146900540214218
T_{57,21} = 16714958004206550
T_{57,22} = 916831645375644
T_{57,23} = 29020363294148
T_{57,24} = 392766537524
T_{57,25} = 999044928
      
T_{58, 1} = 47273309972385997500
T_{58, 2} = 694937893381079040000
T_{58, 3} = 4840670910507951068550
T_{58, 4} = 21249641704420082589696
T_{58, 5} = 65955922468446890821310
T_{58, 6} = 153936621518787241097600
T_{58, 7} = 280486427477292764767626
T_{58, 8} = 408892237454668343022000
T_{58, 9} = 484859118634265971609846
T_{58,10} = 472914114324586740204288
T_{58,11} = 382169255606494341591664
T_{58,12} = 256944517243914868686544
T_{58,13} = 143943726250255355839710
T_{58,14} = 67130932975303518955304
T_{58,15} = 25976926279536884347664
T_{58,16} = 8291259580302866130600
T_{58,17} = 2163484963695435107708
T_{58,18} = 455739946000560861760
T_{58,19} = 76160455123093948230
T_{58,20} = 9854822305933284620
T_{58,21} = 953821651728289406
T_{58,22} = 65590055928567504
T_{58,23} = 2950385151372890
T_{58,24} = 74642228320048
T_{58,25} = 741435997896
      
T_{59, 1} = 46384713920273478750
T_{59, 2} = 681180051982123008000
T_{59, 3} = 4738266671517265708584
T_{59, 4} = 20762994178969867376640
T_{59, 5} = 64302051774822018235488
T_{59, 6} = 149668706158436535119008
T_{59, 7} = 271816205998489923325360
T_{59, 8} = 394699313317995397061760
T_{59, 9} = 465842820434833656063900
T_{59,10} = 451839073678985754119442
T_{59,11} = 362716202894368533864576
T_{59,12} = 241929256048155175573470
T_{59,13} = 134236459361518162043984
T_{59,14} = 61878135773787262244730
T_{59,15} = 23604857677051312142976
T_{59,16} = 7402215107872635982846
T_{59,17} = 1889263827482596431804
T_{59,18} = 386977489985540873228
T_{59,19} = 62382328324809182400
T_{59,20} = 7701822120100332510
T_{59,21} = 700515452849311748
T_{59,22} = 44310648175660124
T_{59,23} = 1779524312252472
T_{59,24} = 38691099997200
T_{59,25} = 323955306976
      
T_{60, 1} = 7172036455810561335000
T_{60, 2} = 106881887767376691200000
T_{60, 3} = 755317979732019544318224
T_{60, 4} = 3366728392297540607705088
T_{60, 5} = 10620506342965462263432750
T_{60, 6} = 25218202906722173261742720
T_{60, 7} = 46801700309724381113388280
T_{60, 8} = 69581555325975211160337488
T_{60, 9} = 84269016496967603025751158
T_{60,10} = 84085890694228871934953900
T_{60,11} = 69649314700071377463837330
T_{60,12} = 48104893579797859995221952
T_{60,13} = 27756913048568642160354482
T_{60,14} = 13374750671285567874040576
T_{60,15} = 5367451724780853111450840
T_{60,16} = 1784884868456815937302656
T_{60,17} = 488000109437304193624778
T_{60,18} = 108485425010823235094328
T_{60,19} = 19310408993068620371866
T_{60,20} = 2694523336043626762000
T_{60,21} = 286139979903397457136
T_{60,22} = 22158270083608093940
T_{60,23} = 1173103801537700312
T_{60,24} = 38271452943063384
T_{60,25} = 643805278584020
T_{60,26} = 4211395943040
      
T_{61, 1} = 2735098648402332712500
T_{61, 2} = 41866367212459130880000
T_{61, 3} = 304317275035227706007910
T_{61, 4} = 1397326150139499051466752
T_{61, 5} = 4548250783578496148584640
T_{61, 6} = 11163666513916025569574400
T_{61, 7} = 21458997216311932266903864
T_{61, 8} = 33116782841428817340211068
T_{61, 9} = 41733412020833876118676056
T_{61,10} = 43449036763562743495820844
T_{61,11} = 37665278883343127642143800
T_{61,12} = 27320273910957818321812624
T_{61,13} = 16621136665712289766605888
T_{61,14} = 8483271530761812192027230
T_{61,15} = 3625548653874657295893460
T_{61,16} = 1292204081376385398288180
T_{61,17} = 381624672563084171873432
T_{61,18} = 92527004799550978072398
T_{61,19} = 18183401935510214048940
T_{61,20} = 2846196073837363663940
T_{61,21} = 346374744132880984960
T_{61,22} = 31665363014275482024
T_{61,23} = 2065229694057101948
T_{61,24} = 88307758456748862
T_{61,25} = 2107871312421240
T_{61,26} = 18580339890000
      
T_{62, 1} = 2782255521650648793750
T_{62, 2} = 42506854071738040320000
T_{62, 3} = 308219352480428564068740
T_{62, 4} = 1410955131479905939931136
T_{62, 5} = 4575648816338274412194490
T_{62, 6} = 11181029431033261849464576
T_{62, 7} = 21378713407128058530571720
T_{62, 8} = 32786657547190443391112800
T_{62, 9} = 41013714499377556027168998
T_{62,10} = 42332011604221689670352700
T_{62,11} = 36327384119432808887575944
T_{62,12} = 26039788731755739309050880
T_{62,13} = 15624224586941070459678686
T_{62,14} = 7846057378225857382842664
T_{62,15} = 3289837891801289113191960
T_{62,16} = 1146429305955177651825968
T_{62,17} = 329634313868880576038532
T_{62,18} = 77403017597165225789040
T_{62,19} = 14633737991630947457478
T_{62,20} = 2184553533756865336160
T_{62,21} = 250614699534668013714
T_{62,22} = 21249461026917082036
T_{62,23} = 1254736608796553160
T_{62,24} = 46682007418970496
T_{62,25} = 894775876979880
T_{62,26} = 4797846206208
      
T_{63, 1} = 6454832810229505201500
T_{63, 2} = 101479745604449730560000
T_{63, 3} = 758359529896942619426430
T_{63, 4} = 3583862405128548619517952
T_{63, 5} = 12020350680572034225963516
T_{63, 6} = 30441301838748972952341312
T_{63, 7} = 60460554340478638936865400
T_{63, 8} = 96562385079408348724102448
T_{63, 9} = 126157179078124424405177800
T_{63,10} = 136440419097769533814257566
T_{63,11} = 123145962884612610065808818
T_{63,12} = 93239658831338377072545920
T_{63,13} = 59388805480251833797951586
T_{63,14} = 31844914813082050394866382
T_{63,15} = 14356787307337642997773298
T_{63,16} = 5424281586364821880425072
T_{63,17} = 1708253818431542113132864
T_{63,18} = 444921590320931934048288
T_{63,19} = 94808007141796298131854
T_{63,20} = 16289193840160052140508
T_{63,21} = 2212476722708180418418
T_{63,22} = 231206335119245971824
T_{63,23} = 17885328921867862932
T_{63,24} = 966286403472221448
T_{63,25} = 33110954699554528
T_{63,26} = 595888229937052
T_{63,27} = 3326409671040
      
T_{64, 1} = 2689513670928960500625
T_{64, 2} = 43177833345455226880000
T_{64, 3} = 329689835733621529757745
T_{64, 4} = 1592939415925724366241792
T_{64, 5} = 5465931244308064600331668
T_{64, 6} = 14171131688640743533408512
T_{64, 7} = 28834815910410635247798180
T_{64, 8} = 47215130740390443744367176
T_{64, 9} = 63292669214262524867821641
T_{64,10} = 70292540991806725613305652
T_{64,11} = 65205616129239317245202789
T_{64,12} = 50787451060035369572768656
T_{64,13} = 33309135225983918652216886
T_{64,14} = 18409235736997835646559960
T_{64,15} = 8563442100194093954615362
T_{64,16} = 3342077285421926452294482
T_{64,17} = 1088514464572527981679868
T_{64,18} = 293593565515446717727920
T_{64,19} = 64883565054782942543074
T_{64,20} = 11581742339715310797890
T_{64,21} = 1637896596817616456928
T_{64,22} = 178746935978137889650
T_{64,23} = 14506248091842030276
T_{64,24} = 828847328685950690
T_{64,25} = 30539606179246778
T_{64,26} = 616812542484936
T_{64,27} = 4573930475520
      
T_{65, 1} = 3912019884987578910000
T_{65, 2} = 63396729426647239884800
T_{65, 3} = 488966528537233679131650
T_{65, 4} = 2388126112323226458882048
T_{65, 5} = 8290028242502568839494482
T_{65, 6} = 21762953906488938098002432
T_{65, 7} = 44883300933618626588007632
T_{65, 8} = 74574438531445856410156664
T_{65, 9} = 101567685440074061934275734
T_{65,10} = 114772151436077005725020900
T_{65,11} = 108509409528733859273559034
T_{65,12} = 86307068475122453870023348
T_{65,13} = 57938571377739243399466068
T_{65,14} = 32866911381781216291773514
T_{65,15} = 15745255731093162528423386
T_{65,16} = 6354632259298654233890614
T_{65,17} = 2151398768742144543573736
T_{65,18} = 607140998534623384439776
T_{65,19} = 141582334785652600899134
T_{65,20} = 26966502580161499543474
T_{65,21} = 4130915207478783560456
T_{65,22} = 498599913983536071074
T_{65,23} = 46107423771812869346
T_{65,24} = 3139208699087455892
T_{65,25} = 148182381362523522
T_{65,26} = 4391291710106020
T_{65,27} = 67965746162800
T_{65,28} = 381125606400
      
T_{66, 1} = 388485308023072072312500
T_{66, 2} = 6354573142635193984614400
T_{66, 3} = 49522489948159083841252680
T_{66, 4} = 244668485271876786571530240
T_{66, 5} = 860214489837458660146666734
T_{66, 6} = 2290199819821742159028869760
T_{66, 7} = 4796957620607103092547757620
T_{66, 8} = 8107132972802865208589416996
T_{66, 9} = 11250034090770844893604695510
T_{66,10} = 12975950080058963658067707104
T_{66,11} = 12546458365089920836769740800
T_{66,12} = 10227424184609149256099563368
T_{66,13} = 7052485878865369323528343750
T_{66,14} = 4119595698991907132649314144
T_{66,15} = 2037588585408114350371583736
T_{66,16} = 851462467440950207188971100
T_{66,17} = 299386771321510438956676496
T_{66,18} = 88035998291582836033743168
T_{66,19} = 21466374233287778616637126
T_{66,20} = 4291179995154095190051784
T_{66,21} = 692700091847662818383730
T_{66,22} = 88493151031956131214776
T_{66,23} = 8705285626349441581822
T_{66,24} = 634505147532911648448
T_{66,25} = 32345632488281864760
T_{66,26} = 1047539321353863440
T_{66,27} = 17732043088389552
T_{66,28} = 84730285078992

T_{67,  1} = 177507902281311393041250
T_{67,  2} = 2934140305335753113600000
T_{67,  3} = 23120202849068433769784640
T_{67,  4} = 115569965705282114537226240
T_{67,  5} = 411415863613916659138736572
T_{67,  6} = 1110040022794347524254469248
T_{67,  7} = 2358678868482764165504364600
T_{67,  8} = 4048815941789210643539213364
T_{67,  9} = 5714497888460773543833561556
T_{67, 10} = 6714788353556968050099915672
T_{67, 11} = 6626816663821679497801749232
T_{67, 12} = 5525838195114432664901708320
T_{67, 13} = 3907853239525834913586924912
T_{67, 14} = 2348098848187728986018375462
T_{67, 15} = 1198845842948568207547112400
T_{67, 16} = 519245473276873482553642176
T_{67, 17} = 190141845715255914153054000
T_{67, 18} = 58557081926086716913441830
T_{67, 19} = 15052781546911859564415072
T_{67, 20} = 3197106999693046789111158
T_{67, 21} = 553440640537384318563224
T_{67, 22} = 76669222909551515245890
T_{67, 23} = 8291570002948969786280
T_{67, 24} = 676254662528716729670
T_{67, 25} = 39556423172570471664
T_{67, 26} = 1534591259041241588
T_{67, 27} = 34431525297050400
T_{67, 28} = 327215454658560

T_{68,  1} = 186472947851074594710000
T_{68,  2} = 3141831719985159864320000
T_{68,  3} = 25259103506412258726801096
T_{68,  4} = 128954425624546160622993408
T_{68,  5} = 469353387288165475616574430
T_{68,  6} = 1296199516372068062155004160
T_{68,  7} = 2822471078167995183782874702
T_{68,  8} = 4971177427271631355641990648
T_{68,  9} = 7208705827088424371111270430
T_{68, 10} = 8715199866516799848059394240
T_{68, 11} = 8863025014408198201495753210
T_{68, 12} = 7628386877491427457349688928
T_{68, 13} = 5578662660614820256180469088
T_{68, 14} = 3473442165090667268258071832
T_{68, 15} = 1841944396004714898845507514
T_{68, 16} = 830874891251715849168044500
T_{68, 17} = 317898779154852925939932596
T_{68, 18} = 102691533911057385585597408
T_{68, 19} = 27824229313563528726640468
T_{68, 20} = 6267579448164981400912976
T_{68, 21} = 1160008799694767332928280
T_{68, 22} = 173689145293033034053928
T_{68, 23} = 20608612808598906381540
T_{68, 24} = 1883593860154046423712
T_{68, 25} = 127336879745643358266
T_{68, 26} = 5979193793336115360
T_{68, 27} = 174479755893847560
T_{68, 28} = 2454993810416256
T_{68, 29} = 4459536000000

T_{69, 1} =  366286147564610811037500
T_{69, 2} =  6211310944496555078451200
T_{69, 3} =  50262362124461098485940080
T_{69, 4} =  258298936132928392150941696
T_{69, 5} =  946441951280640594245603678
T_{69, 6} =  2631668353319522416845904128
T_{69, 7} =  5770657980444642802688944674
T_{69, 8} =  10237154682060217094463545952
T_{69, 9} =  14955771352580870491128404702
T_{69, 10} = 18221809610387449589332698992
T_{69, 11} = 18681799474696052531694348314
T_{69, 12} = 16217617219451753673969607406
T_{69, 13} = 11968510037633146245939975676
T_{69, 14} = 7525180991636531242427667566
T_{69, 15} = 4033090229600314325382330486
T_{69, 16} = 1840531143434228708049557332
T_{69, 17} = 713331738079914442663183672
T_{69, 18} = 233787519610806718870527864
T_{69, 19} = 64397321255737263529777340
T_{69, 20} = 14785183861867972514695022
T_{69, 21} = 2798603021932905175551048
T_{69, 22} = 430498670540718539274460
T_{69, 23} = 52804363130808404955190
T_{69, 24} = 5033822296558256420134
T_{69, 25} = 359786341021827724360
T_{69, 26} = 18275562895189599412
T_{69, 27} = 604380014074491416
T_{69, 28} = 10997597613113760
T_{69, 29} = 70977249747200

T_{70,  1} = 19299950102586220552485000
T_{70,  2} = 331126639823017947955200000
T_{70,  3} = 2713744597425605094989303820
T_{70,  4} = 14139911619257864578718367744
T_{70,  5} = 52595306809343807888270778120
T_{70,  6} = 148661499457467249542544375808
T_{70,  7} = 331859509626180101177832272514
T_{70,  8} = 600326449500119644708781753504
T_{70,  9} = 895972431134846973291260363918
T_{70, 10} = 1117496135509475133802404070680
T_{70, 11} = 1175547737535258227281572620122
T_{70, 12} = 1049781353294709372899448022312
T_{70, 13} = 799303626721118870343217005330
T_{70, 14} = 520225212769076622570289067856
T_{70, 15} = 289711004129914517925389882300
T_{70, 16} = 137982169659053427063495562908
T_{70, 17} = 56095900950505493364058621298
T_{70, 18} = 19400383829056979646344866952
T_{70, 19} = 5679137256505968057604972500
T_{70, 20} = 1397579221984791280988687600
T_{70, 21} = 286539310949866856798127050
T_{70, 22} = 48377344392102248445227808
T_{70, 23} = 6625212556065380268525368
T_{70, 24} = 721602172400366229149144
T_{70, 25} = 60880877692352633689110
T_{70, 26} = 3834797432826979514632
T_{70, 27} = 170603170650266776258
T_{70, 28} = 4875753099385661304
T_{70, 29} = 73128822623672616
T_{70, 30} = 282125323468800

INRIA, Domaine de Voluceau - Rocquencourt, 78153 Le Chesnay, France.

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