*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St001599
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(mu):
s = SymmetricFunctions(QQ).s()
A = CombinatorialSpecies()
X = species.SingletonSpecies()
E = species.SetSpecies()
A.define(X*E(A))
F = A.cycle_index_series()
return F.coefficient(mu.size()).scalar(s(mu))
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[2] => 1
[1,1] => 1
[3] => 2
[2,1] => 3
[1,1,1] => 1
[4] => 4
[3,1] => 9
[2,2] => 5
[2,1,1] => 7
[1,1,1,1] => 2
[5] => 9
[4,1] => 26
[3,2] => 28
[3,1,1] => 30
[2,2,1] => 24
[2,1,1,1] => 17
[1,1,1,1,1] => 4
[6] => 20
[5,1] => 75
[4,2] => 114
[4,1,1] => 117
[3,3] => 59
[3,2,1] => 170
[3,1,1,1] => 96
[2,2,2] => 49
[2,2,1,1] => 83
[2,1,1,1,1] => 42
[1,1,1,1,1,1] => 8
[7] => 48
[6,1] => 214
[5,2] => 421
[5,1,1] => 419
[4,3] => 382
[4,2,1] => 874
[4,1,1,1] => 459
[3,3,1] => 493
[3,2,2] => 474
[3,2,1,1] => 745
[3,1,1,1,1] => 294
[2,2,2,1] => 281
[2,2,1,1,1] => 261
[2,1,1,1,1,1] => 104
[1,1,1,1,1,1,1] => 16
[8] => 115
[7,1] => 612
[6,2] => 1462
[6,1,1] => 1446
[5,3] => 1833
[5,2,1] => 3875
[5,1,1,1] => 1966
[4,4] => 868
[4,3,1] => 3930
[4,2,2] => 3014
[4,2,1,1] => 4619
[4,1,1,1,1] => 1657
[3,3,2] => 2154
[3,3,1,1] => 2742
[3,2,2,1] => 3309
[3,2,1,1,1] => 2847
[3,1,1,1,1,1] => 863
[2,2,2,2] => 615
[2,2,2,1,1] => 1181
[2,2,1,1,1,1] => 789
[2,1,1,1,1,1,1] => 257
[1,1,1,1,1,1,1,1] => 34
[9] => 286
[8,1] => 1747
[7,2] => 4918
[7,1,1] => 4834
[6,3] => 7733
[6,2,1] => 15795
[6,1,1,1] => 7881
[5,4] => 6309
[5,3,1] => 22276
[5,2,2] => 15880
[5,2,1,1] => 23968
[5,1,1,1,1] => 8243
[4,4,1] => 11068
[4,3,2] => 20851
[4,3,1,1] => 25758
[4,2,2,1] => 24878
[4,2,1,1,1] => 20609
[4,1,1,1,1,1] => 5646
[3,3,3] => 4901
[3,3,2,1] => 18597
[3,3,1,1,1] => 12607
[3,2,2,2] => 8857
[3,2,2,1,1] => 16474
[3,2,1,1,1,1] => 10041
[3,1,1,1,1,1,1] => 2473
[2,2,2,2,1] => 4016
[2,2,2,1,1,1] => 4378
[2,2,1,1,1,1,1] => 2313
[2,1,1,1,1,1,1,1] => 637
[1,1,1,1,1,1,1,1,1] => 75
[10] => 719
[9,1] => 4995
[8,2] => 16146
[8,1,1] => 15857
[7,3] => 30362
[7,2,1] => 60900
[7,1,1,1] => 30112
[6,4] => 33498
[6,3,1] => 108412
[6,2,2] => 74709
[6,2,1,1] => 111911
[6,1,1,1,1] => 37600
[5,5] => 15006
[5,4,1] => 93468
[5,3,2] => 138409
[5,3,1,1] => 168245
[5,2,2,1] => 150801
[5,2,1,1,1] => 122417
[5,1,1,1,1,1] => 31950
[4,4,2] => 74669
[4,4,1,1] => 85834
[4,3,3] => 60063
[4,3,2,1] => 209063
[4,3,1,1,1] => 136189
[4,2,2,2] => 77965
[4,2,2,1,1] => 142719
[4,2,1,1,1,1] => 83113
[4,1,1,1,1,1,1] => 18455
[3,3,3,1] => 54317
[3,3,2,2] => 63287
[3,3,2,1,1] => 109553
[3,3,1,1,1,1] => 51744
[3,2,2,2,1] => 67184
[3,2,2,1,1,1] => 70417
[3,2,1,1,1,1,1] => 33588
[3,1,1,1,1,1,1,1] => 6994
[2,2,2,2,2] => 9137
[2,2,2,2,1,1] => 19047
[2,2,2,1,1,1,1] => 15109
[2,2,1,1,1,1,1,1] => 6619
[2,1,1,1,1,1,1,1,1] => 1586
[1,1,1,1,1,1,1,1,1,1] => 166
[11] => 1842
[10,1] => 14294
[9,2] => 52188
[9,1,1] => 51198
[8,3] => 113682
[8,2,1] => 225817
[8,1,1,1] => 111100
[7,4] => 155126
[7,3,1] => 481703
[7,2,2] => 326253
[7,2,1,1] => 486387
[7,1,1,1,1] => 161328
[6,5] => 117380
[6,4,1] => 565246
[6,3,2] => 768853
[6,3,1,1] => 926155
[6,2,2,1] => 802176
[6,2,1,1,1] => 643560
[6,1,1,1,1,1] => 163526
[5,5,1] => 259844
[5,4,2] => 730560
[5,4,1,1] => 825653
[5,3,3] => 471677
[5,3,2,1] => 1577580
[5,3,1,1,1] => 1006100
[5,2,2,2] => 539526
[5,2,2,1,1] => 978015
[5,2,1,1,1,1] => 555595
[5,1,1,1,1,1,1] => 117102
[4,4,3] => 319567
[4,4,2,1] => 872849
[4,4,1,1,1] => 522151
[4,3,3,1] => 762112
[4,3,2,2] => 823458
[4,3,2,1,1] => 1400739
[4,3,1,1,1,1] => 632258
[4,2,2,2,1] => 672645
[4,2,2,1,1,1] => 689628
[4,2,1,1,1,1,1] => 312922
[4,1,1,1,1,1,1,1] => 58522
[3,3,3,2] => 275496
[3,3,3,1,1] => 382999
[3,3,2,2,1] => 559655
[3,3,2,1,1,1] => 538355
[3,3,1,1,1,1,1] => 197143
[3,2,2,2,2] => 177253
[3,2,2,2,1,1] => 362854
[3,2,2,1,1,1,1] => 274761
[3,2,1,1,1,1,1,1] => 108250
[3,1,1,1,1,1,1,1,1] => 19561
[2,2,2,2,2,1] => 64977
[2,2,2,2,1,1,1] => 78474
[2,2,2,1,1,1,1,1] => 49699
[2,2,1,1,1,1,1,1,1] => 18650
[2,1,1,1,1,1,1,1,1,1] => 3959
[1,1,1,1,1,1,1,1,1,1,1] => 370
[12] => 4766
[11,1] => 40967
[10,2] => 166593
[10,1,1] => 163477
[9,3] => 411740
[9,2,1] => 813242
[9,1,1,1] => 398984
[8,4] => 662870
[8,3,1] => 2013446
[8,2,2] => 1350027
[8,2,1,1] => 2007267
[8,1,1,1,1] => 660569
[7,5] => 669168
[7,4,1] => 2932280
[7,3,2] => 3832294
[7,3,1,1] => 4591051
[7,2,2,1] => 3904901
[7,2,1,1,1] => 3110383
[7,1,1,1,1,1] => 777944
[6,6] => 287646
[6,5,1] => 2292196
[6,4,2] => 4998273
[6,4,1,1] => 5594484
[6,3,3] => 2996417
[6,3,2,1] => 9806438
[6,3,1,1,1] => 6176275
[6,2,2,2] => 3218526
[6,2,2,1,1] => 5799947
[6,2,1,1,1,1] => 3246181
[6,1,1,1,1,1,1] => 664489
[5,5,2] => 2393038
[5,5,1,1] => 2616024
[5,4,3] => 3665196
[5,4,2,1] => 9615650
[5,4,1,1,1] => 5629097
[5,3,3,1] => 6733253
[5,3,2,2] => 7027859
[5,3,2,1,1] => 11832377
[5,3,1,1,1,1] => 5208603
[5,2,2,2,1] => 5207109
[5,2,2,1,1,1] => 5268509
[5,2,1,1,1,1,1] => 2324232
[5,1,1,1,1,1,1,1] => 411617
[4,4,4] => 767374
[4,4,3,1] => 4672515
[4,4,2,2] => 4046784
[4,4,2,1,1] => 6654415
[4,4,1,1,1,1] => 2736039
[4,3,3,2] => 4431193
[4,3,3,1,1] => 6048237
[4,3,2,2,1] => 8196079
[4,3,2,1,1,1] => 7708135
[4,3,1,1,1,1,1] => 2687248
[4,2,2,2,2] => 2007817
[4,2,2,2,1,1] => 4067001
[4,2,2,1,1,1,1] => 2999761
[4,2,1,1,1,1,1,1] => 1120777
[4,1,1,1,1,1,1,1,1] => 181323
[3,3,3,3] => 653476
[3,3,3,2,1] => 2880740
[3,3,3,1,1,1] => 2172252
[3,3,2,2,2] => 1737900
[3,3,2,2,1,1] => 3438253
[3,3,2,1,1,1,1] => 2368802
[3,3,1,1,1,1,1,1] => 712438
[3,2,2,2,2,1] => 1419280
[3,2,2,2,1,1,1] => 1674954
[3,2,2,1,1,1,1,1] => 1007873
[3,2,1,1,1,1,1,1,1] => 339353
[3,1,1,1,1,1,1,1,1,1] => 54170
[2,2,2,2,2,2] => 151661
[2,2,2,2,2,1,1] => 334219
[2,2,2,2,1,1,1,1] => 297635
[2,2,2,1,1,1,1,1,1] => 158017
[2,2,1,1,1,1,1,1,1,1] => 51998
[2,1,1,1,1,1,1,1,1,1,1] => 9899
[1,1,1,1,1,1,1,1,1,1,1,1] => 841
[13] => 12486
[12,1] => 117560
[11,2] => 526938
[11,1,1] => 517187
[10,3] => 1454530
[10,2,1] => 2863468
[10,1,1,1] => 1402768
[9,4] => 2684621
[9,3,1] => 8049646
[9,2,2] => 5365056
[9,2,1,1] => 7963420
[9,1,1,1,1] => 2608389
[8,5] => 3312394
[8,4,1] => 13866810
[8,3,2] => 17733622
[8,3,1,1] => 21172350
[8,2,2,1] => 17818309
[8,2,1,1,1] => 14128937
[8,1,1,1,1,1] => 3499254
[7,6] => 2373015
[7,5,1] => 14521026
[7,4,2] => 28864981
[7,4,1,1] => 32116116
[7,3,3] => 16723498
[7,3,2,1] => 54036226
[7,3,1,1,1] => 33770537
[7,2,2,2] => 17340374
[7,2,2,1,1] => 31128235
[7,2,1,1,1,1] => 17260955
[7,1,1,1,1,1,1] => 3470680
[6,6,1] => 6345797
[6,5,2] => 23702675
[6,5,1,1] => 25650810
[6,4,3] => 28460048
[6,4,2,1] => 73035793
[6,4,1,1,1] => 42208136
[6,3,3,1] => 47451871
[6,3,2,2] => 48616209
[6,3,2,1,1] => 81330806
[6,3,1,1,1,1] => 35264276
[6,2,2,2,1] => 34329413
[6,2,2,1,1,1] => 34445325
[6,2,1,1,1,1,1] => 14937254
[6,1,1,1,1,1,1,1] => 2563710
[5,5,3] => 14762478
[5,5,2,1] => 35529815
[5,5,1,1,1] => 19970378
[5,4,4] => 10782449
[5,4,3,1] => 59818074
[5,4,2,2] => 50043270
[5,4,2,1,1] => 81423905
[5,4,1,1,1,1] => 32643245
[5,3,3,2] => 43925679
[5,3,3,1,1] => 59317092
[5,3,2,2,1] => 77619191
[5,3,2,1,1,1] => 72016943
[5,3,1,1,1,1,1] => 24414568
[5,2,2,2,2] => 17300648
[5,2,2,2,1,1] => 34807415
[5,2,2,1,1,1,1] => 25266951
[5,2,1,1,1,1,1,1] => 9156430
[5,1,1,1,1,1,1,1,1] => 1399954
[4,4,4,1] => 13149059
[4,4,3,2] => 31702900
[4,4,3,1,1] => 41807708
[4,4,2,2,1] => 45394673
[4,4,2,1,1,1] => 40962030
[4,4,1,1,1,1,1] => 12937775
[4,3,3,3] => 12227135
[4,3,3,2,1] => 51699039
[4,3,3,1,1,1] => 38100605
[4,3,2,2,2] => 28570505
[4,3,2,2,1,1] => 55907499
[4,3,2,1,1,1,1] => 37522830
[4,3,1,1,1,1,1,1] => 10710735
[4,2,2,2,2,1] => 17843375
[4,2,2,2,1,1,1] => 20762403
[4,2,2,1,1,1,1,1] => 12134332
[4,2,1,1,1,1,1,1,1] => 3865062
[4,1,1,1,1,1,1,1,1,1] => 551430
[3,3,3,3,1] => 8450034
[3,3,3,2,2] => 11024598
[3,3,3,2,1,1] => 20234283
[3,3,3,1,1,1,1] => 10785694
[3,3,2,2,2,1] => 15681116
[3,3,2,2,1,1,1] => 17746031
[3,3,2,1,1,1,1,1] => 9662228
[3,3,1,1,1,1,1,1,1] => 2473578
[3,2,2,2,2,2] => 3721471
[3,2,2,2,2,1,1] => 8108579
[3,2,2,2,1,1,1,1] => 7028312
[3,2,2,1,1,1,1,1,1] => 3535088
[3,2,1,1,1,1,1,1,1,1] => 1041251
[3,1,1,1,1,1,1,1,1,1,1] => 148892
[2,2,2,2,2,2,1] => 1144504
[2,2,2,2,2,1,1,1] => 1485062
[2,2,2,2,1,1,1,1,1] => 1067450
[2,2,2,1,1,1,1,1,1,1] => 489921
[2,2,1,1,1,1,1,1,1,1,1] => 143725
[2,1,1,1,1,1,1,1,1,1,1,1] => 24803
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 1937
[14] => 32973
[13,1] => 337830
[12,2] => 1654257
[12,1,1] => 1624554
[11,3] => 5039926
[11,2,1] => 9902842
[11,1,1,1] => 4847734
[10,4] => 10456926
[10,3,1] => 31108545
[10,2,2] => 20654979
[10,2,1,1] => 30628756
[10,1,1,1,1] => 10003154
[9,5] => 15077304
[9,4,1] => 61538238
[9,3,2] => 77693810
[9,3,1,1] => 92557381
[9,2,2,1] => 77386723
[9,2,1,1,1] => 61186563
[9,1,1,1,1,1] => 15059202
[8,6] => 14249222
[8,5,1] => 78994961
[8,4,2] => 150135855
[8,4,1,1] => 166414274
[8,3,3] => 85407750
[8,3,2,1] => 273766926
[8,3,1,1,1] => 170241639
[8,2,2,2] => 86678879
[8,2,2,1,1] => 155210847
[8,2,1,1,1,1] => 85547356
[8,1,1,1,1,1,1] => 17006324
[7,7] => 5938318
[7,6,1] => 57783051
[7,5,2] => 166091679
[7,5,1,1] => 178617975
[7,4,3] => 182865109
[7,4,2,1] => 463145636
[7,4,1,1,1] => 265495761
[7,3,3,1] => 290670069
[7,3,2,2] => 294560241
[7,3,2,1,1] => 490735466
[7,3,1,1,1,1] => 210742474
[7,2,2,2,1] => 202418417
[7,2,2,1,1,1] => 201992533
[7,2,1,1,1,1,1] => 86634985
[7,1,1,1,1,1,1,1] => 14582319
[6,6,2] => 74283437
[6,6,1,1] => 78949145
[6,5,3] => 164915955
[6,5,2,1] => 388110594
[6,5,1,1,1] => 215279308
[6,4,4] => 96548839
[6,4,3,1] => 511886812
[6,4,2,2] => 420309243
[6,4,2,1,1] => 679358312
[6,4,1,1,1,1] => 268205412
[6,3,3,2] => 342184157
[6,3,3,1,1] => 458988254
[6,3,2,2,1] => 589362757
[6,3,2,1,1,1] => 542133855
[6,3,1,1,1,1,1] => 180657554
[6,2,2,2,2] => 125420661
[6,2,2,2,1,1] => 251217686
[6,2,2,1,1,1,1] => 180494649
[6,2,1,1,1,1,1,1] => 64181517
[6,1,1,1,1,1,1,1,1] => 9493753
[5,5,4] => 62758253
[5,5,3,1] => 269611885
[5,5,2,2] => 209195646
[5,5,2,1,1] => 334158123
[5,5,1,1,1,1] => 127982874
[5,4,4,1] => 204763407
[5,4,3,2] => 452456209
[5,4,3,1,1] => 590211424
[5,4,2,2,1] => 618787954
[5,4,2,1,1,1] => 550754654
[5,4,1,1,1,1,1] => 169152560
[5,3,3,3] => 136666196
[5,3,3,2,1] => 564685782
[5,3,3,1,1,1] => 410439810
[5,3,2,2,2] => 299194543
[5,3,2,2,1,1] => 581416259
[5,3,2,1,1,1,1] => 384016010
[5,3,1,1,1,1,1,1] => 106357366
[5,2,2,2,2,1] => 168752177
[5,2,2,2,1,1,1] => 194582233
[5,2,2,1,1,1,1,1] => 111684023
[5,2,1,1,1,1,1,1,1] => 34441448
[5,1,1,1,1,1,1,1,1,1] => 4636148
[4,4,4,2] => 109175788
[4,4,4,1,1] => 133555377
[4,4,3,3] => 106773534
[4,4,3,2,1] => 413699745
[4,4,3,1,1,1] => 292419408
[4,4,2,2,2] => 178971175
[4,4,2,2,1,1] => 343701813
[4,4,2,1,1,1,1] => 220223262
[4,4,1,1,1,1,1,1] => 56731883
[4,3,3,3,1] => 175138306
[4,3,3,2,2] => 220601134
[4,3,3,2,1,1] => 400371062
[4,3,3,1,1,1,1] => 207879257
[4,3,2,2,2,1] => 284131158
[4,3,2,2,1,1,1] => 317001906
[4,3,2,1,1,1,1,1] => 167689187
[4,3,1,1,1,1,1,1,1] => 40646984
[4,2,2,2,2,2] => 51754089
[4,2,2,2,2,1,1] => 111953052
[4,2,2,2,1,1,1,1] => 95426777
[4,2,2,1,1,1,1,1,1] => 46517150
[4,2,1,1,1,1,1,1,1,1] => 12937639
[4,1,1,1,1,1,1,1,1,1,1] => 1651612
[3,3,3,3,2] => 46932665
[3,3,3,3,1,1] => 69026719
[3,3,3,2,2,1] => 112807355
[3,3,3,2,1,1,1] => 116948640
[3,3,3,1,1,1,1,1] => 48874832
[3,3,2,2,2,2] => 46507230
[3,3,2,2,2,1,1] => 99421226
[3,3,2,2,1,1,1,1] => 82211205
[3,3,2,1,1,1,1,1,1] => 37274049
[3,3,1,1,1,1,1,1,1,1] => 8322668
[3,2,2,2,2,2,1] => 30960925
[3,2,2,2,2,1,1,1] => 39587695
[3,2,2,2,1,1,1,1,1] => 27617045
[3,2,2,1,1,1,1,1,1,1] => 11982968
[3,2,1,1,1,1,1,1,1,1,1] => 3140626
[3,1,1,1,1,1,1,1,1,1,1,1] => 406926
[2,2,2,2,2,2,2] => 2719750
[2,2,2,2,2,2,1,1] => 6240983
[2,2,2,2,2,1,1,1,1] => 6043832
[2,2,2,2,1,1,1,1,1,1] => 3675528
[2,2,2,1,1,1,1,1,1,1,1] => 1489539
[2,2,1,1,1,1,1,1,1,1,1,1] => 394399
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 62277
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 4488
[15] => 87811
[14,1] => 972027
[13,2] => 5162510
[13,1,1] => 5072470
[12,3] => 17194564
[12,2,1] => 33749476
[12,1,1,1] => 16517440
[11,4] => 39536708
[11,3,1] => 117034850
[11,2,2] => 77519018
[11,2,1,1] => 114886192
[11,1,1,1,1] => 37456239
[10,5] => 64818488
[10,4,1] => 260559486
[10,3,2] => 326328078
[10,3,1,1] => 388214926
[10,2,2,1] => 323217583
[10,2,1,1,1] => 255082332
[10,1,1,1,1,1] => 62526377
[9,6] => 74188203
[9,5,1] => 391657956
[9,4,2] => 725990084
[9,4,1,1] => 802704875
[9,3,3] => 408562603
[9,3,2,1] => 1302839869
[9,3,1,1,1] => 807510347
[9,2,2,2] => 409009574
[9,2,2,1,1] => 731162883
[9,2,1,1,1,1] => 401385752
[9,1,1,1,1,1,1] => 79195818
[8,7] => 50965136
[8,6,1] => 379122068
[8,5,2] => 988331785
[8,5,1,1] => 1058562658
[8,4,3] => 1043986974
[8,4,1,1,1] => 1495221953
[8,3,3,1] => 1615236170
[8,3,2,2] => 1625643526
[8,3,1,1,1,1] => 1152516097
[8,2,2,2,1] => 1098655937
[8,2,2,1,1,1] => 1092312951
[8,2,1,1,1,1,1] => 465080787
[8,1,1,1,1,1,1,1] => 77293835
[7,7,1] => 159750388
[7,6,2] => 744172569
[7,6,1,1] => 785771135
[7,5,3] => 1278904432
[7,5,1,1,1] => 1633379117
[7,4,4] => 694421799
[7,4,1,1,1,1] => 1833656854
[7,3,1,1,1,1,1] => 1171129666
[7,2,2,2,2] => 805562674
[7,2,2,2,1,1] => 1608676864
[7,2,2,1,1,1,1] => 1147891361
[7,2,1,1,1,1,1,1] => 403148722
[7,1,1,1,1,1,1,1,1] => 58405033
[6,6,3] => 594561395
[6,6,2,1] => 1342465290
[6,6,1,1,1] => 727953397
[6,5,4] => 804252594
[6,5,1,1,1,1] => 1503500213
[6,4,4,1] => 2008573926
[6,4,1,1,1,1,1] => 1510677178
[6,3,3,3] => 1177946350
[6,3,1,1,1,1,1,1] => 853700235
[6,2,2,2,2,1] => 1331035536
[6,2,2,2,1,1,1] => 1525453458
[6,2,2,1,1,1,1,1] => 865269336
[6,2,1,1,1,1,1,1,1] => 261447141
[6,1,1,1,1,1,1,1,1,1] => 34004305
[5,5,5] => 155371996
[5,5,4,1] => 1325076561
[5,5,1,1,1,1,1] => 725509751
[5,4,4,2] => 1884385521
[5,4,3,3] => 1708792896
[5,4,1,1,1,1,1,1] => 806327926
[5,3,3,3,1] => 2143806319
[5,3,2,1,1,1,1,1] => 1864999798
[5,3,1,1,1,1,1,1,1] => 437864205
[5,2,2,2,2,2] => 535343174
[5,2,2,2,2,1,1] => 1152435786
[5,2,2,2,1,1,1,1] => 971636938
[5,2,2,1,1,1,1,1,1] => 464388438
[5,2,1,1,1,1,1,1,1,1] => 124863051
[5,1,1,1,1,1,1,1,1,1,1] => 15020917
[4,4,4,3] => 529303489
[4,4,4,2,1] => 1605699258
[4,4,4,1,1,1] => 1039872691
[4,4,3,3,1] => 1699418976
[4,4,3,2,2] => 1984352702
[4,4,3,1,1,1,1] => 1751211917
[4,4,2,2,2,1] => 1962392850
[4,4,2,2,1,1,1] => 2138583579
[4,4,2,1,1,1,1,1] => 1076174044
[4,4,1,1,1,1,1,1,1] => 234751233
[4,3,3,3,2] => 1078157705
[4,3,3,3,1,1] => 1567775172
[4,3,3,1,1,1,1,1] => 1026160738
[4,3,2,2,2,2] => 926836436
[4,3,2,2,2,1,1] => 1966898497
[4,3,2,2,1,1,1,1] => 1599536383
[4,3,2,1,1,1,1,1,1] => 703125821
[4,3,1,1,1,1,1,1,1,1] => 148387203
[4,2,2,2,2,2,1] => 469936718
[4,2,2,2,2,1,1,1] => 595145513
[4,2,2,2,1,1,1,1,1] => 407483258
[4,2,2,1,1,1,1,1,1,1] => 171059312
[4,2,1,1,1,1,1,1,1,1,1] => 42274159
[4,1,1,1,1,1,1,1,1,1,1,1] => 4884926
[3,3,3,3,3] => 113973816
[3,3,3,3,2,1] => 554525027
[3,3,3,3,1,1,1] => 449972148
[3,3,3,2,2,2] => 385501205
[3,3,3,2,2,1,1] => 795561721
[3,3,3,2,1,1,1,1] => 598052628
[3,3,3,1,1,1,1,1,1] => 207033802
[3,3,2,2,2,2,1] => 426563586
[3,3,2,2,2,1,1,1] => 532543453
[3,3,2,2,1,1,1,1,1] => 353150826
[3,3,2,1,1,1,1,1,1,1] => 137739677
[3,3,1,1,1,1,1,1,1,1,1] => 27305619
[3,2,2,2,2,2,2] => 80958568
[3,2,2,2,2,2,1,1] => 184371259
[3,2,2,2,2,1,1,1,1] => 175492754
[3,2,2,2,1,1,1,1,1,1] => 103369125
[3,2,2,1,1,1,1,1,1,1,1] => 39535615
[3,2,1,1,1,1,1,1,1,1,1,1] => 9341114
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 1106787
[2,2,2,2,2,2,2,1] => 21438058
[2,2,2,2,2,2,1,1,1] => 29344677
[2,2,2,2,2,1,1,1,1,1] => 23159883
[2,2,2,2,1,1,1,1,1,1,1] => 12268309
[2,2,2,1,1,1,1,1,1,1,1,1] => 4458118
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 1076106
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 156635
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 10470
[16] => 235381
[15,1] => 2800210
[14,2] => 16030711
[14,1,1] => 15760718
[13,3] => 57922032
[13,2,1] => 113629123
[13,1,1,1] => 55614698
[12,4] => 145993458
[12,3,1] => 430796257
[12,2,2] => 284890592
[12,2,1,1] => 422103925
[12,1,1,1,1] => 137481101
[11,5] => 267178895
[11,4,1] => 1063722818
[11,3,2] => 1325271009
[11,3,1,1] => 1575196622
[11,2,2,1] => 1307806764
[11,2,1,1,1] => 1030906484
[11,1,1,1,1,1] => 252034735
[10,6] => 354580296
[10,5,1] => 1820774416
[10,3,3] => 1858162722
[10,2,2,2] => 1843448903
[10,2,1,1,1,1] => 1802234216
[10,1,1,1,1,1,1] => 353805825
[9,7] => 318473957
[9,6,1] => 2139325004
[9,1,1,1,1,1,1,1] => 387162287
[8,8] => 129535248
[8,7,1] => 1490784962
[8,1,1,1,1,1,1,1,1] => 332915234
[7,2,1,1,1,1,1,1,1] => 1767866133
[7,1,1,1,1,1,1,1,1,1] => 224946705
[6,2,1,1,1,1,1,1,1,1] => 1020358944
[6,1,1,1,1,1,1,1,1,1,1] => 118477879
[5,3,1,1,1,1,1,1,1,1] => 1723206656
[5,2,2,1,1,1,1,1,1,1] => 1840737571
[5,2,1,1,1,1,1,1,1,1,1] => 439255517
[5,1,1,1,1,1,1,1,1,1,1,1] => 47785430
[4,4,4,4] => 1306046046
[4,4,1,1,1,1,1,1,1,1] => 927611299
[4,3,1,1,1,1,1,1,1,1,1] => 524922173
[4,2,2,2,2,2,2] => 1337861000
[4,2,2,2,1,1,1,1,1,1] => 1646507663
[4,2,2,1,1,1,1,1,1,1,1] => 608446614
[4,2,1,1,1,1,1,1,1,1,1,1] => 135403979
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 14295748
[3,3,3,3,3,1] => 1631749681
[3,3,3,1,1,1,1,1,1,1] => 832477037
[3,3,2,2,2,2,2] => 1231379074
[3,3,2,2,1,1,1,1,1,1] => 1433601427
[3,3,2,1,1,1,1,1,1,1,1] => 491833726
[3,3,1,1,1,1,1,1,1,1,1,1] => 87751048
[3,2,2,2,2,2,2,1] => 693138608
[3,2,2,2,2,2,1,1,1] => 939406998
[3,2,2,2,2,1,1,1,1,1] => 727322272
[3,2,2,2,1,1,1,1,1,1,1] => 372574501
[3,2,2,1,1,1,1,1,1,1,1,1] => 127604626
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 27461558
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2997745
[2,2,2,2,2,2,2,2] => 51631096
[2,2,2,2,2,2,2,1,1] => 122192606
[2,2,2,2,2,2,1,1,1,1] => 126113655
[2,2,2,2,2,1,1,1,1,1,1] => 84885341
[2,2,2,2,1,1,1,1,1,1,1,1] => 39952525
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 13172019
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 2922614
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 394541
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 24617
[17] => 634847
[16,1] => 8075889
[15,2] => 49573027
[15,1,1] => 48766303
[14,3] => 193057849
[14,2,1] => 378664173
[14,1,1,1] => 185378712
[13,4] => 528810821
[13,3,1] => 1557249811
[13,2,2] => 1028777845
[13,2,1,1] => 1524130518
[13,1,1,1,1] => 496169063
[12,5] => 1065941036
[12,1,1,1,1,1] => 990929161
[11,6] => 1597860048
[11,1,1,1,1,1,1] => 1526944296
[10,7] => 1725014317
[10,1,1,1,1,1,1,1] => 1851293429
[9,8] => 1146402753
[9,1,1,1,1,1,1,1,1] => 1784473033
[8,1,1,1,1,1,1,1,1,1] => 1371962305
[7,1,1,1,1,1,1,1,1,1,1] => 838596407
[6,1,1,1,1,1,1,1,1,1,1,1] => 403313023
[5,2,1,1,1,1,1,1,1,1,1,1] => 1507004012
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 149673796
[4,3,1,1,1,1,1,1,1,1,1,1] => 1809106792
[4,2,2,1,1,1,1,1,1,1,1,1] => 2105875810
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 426488173
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 41459188
[3,3,2,1,1,1,1,1,1,1,1,1] => 1707635704
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 277153166
[3,2,2,2,2,2,2,2] => 1810230869
[3,2,2,2,1,1,1,1,1,1,1,1] => 1302782039
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 404412154
-----------------------------------------------------------------------------
Created: Sep 26, 2020 at 23:49 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 26, 2020 at 23:49 by Martin Rubey