# 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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