From: David W. Wilson (wilson(AT)aprisma.com)
Date: Fri, 07 Sep 2001 15:59:49 -0400

Extended tables for A008304 and A064315.

EIS sequence A008304

f(n,k) = number of permutations of {1,...,n} whose longest run of
increasing adjacent elements is of length k.

f(1,1) = 1

f(2,1) = 1
f(2,2) = 1

f(3,1) = 1
f(3,2) = 4
f(3,3) = 1

f(4,1) = 1
f(4,2) = 16
f(4,3) = 6
f(4,4) = 1

f(5,1) = 1
f(5,2) = 69
f(5,3) = 41
f(5,4) = 8
f(5,5) = 1

f(6,1) = 1
f(6,2) = 348
f(6,3) = 293
f(6,4) = 67
f(6,5) = 10
f(6,6) = 1

f(7,1) = 1
f(7,2) = 2016
f(7,3) = 2309
f(7,4) = 602
f(7,5) = 99
f(7,6) = 12
f(7,7) = 1

f(8,1) = 1
f(8,2) = 13357
f(8,3) = 19975
f(8,4) = 5811
f(8,5) = 1024
f(8,6) = 137
f(8,7) = 14
f(8,8) = 1

f(9,1) = 1
f(9,2) = 99376
f(9,3) = 189524
f(9,4) = 60875
f(9,5) = 11304
f(9,6) = 1602
f(9,7) = 181
f(9,8) = 16
f(9,9) = 1

f(10,1) = 1
f(10,2) = 822040
f(10,3) = 1960041
f(10,4) = 690729
f(10,5) = 133669
f(10,6) = 19710
f(10,7) = 2360
f(10,8) = 231
f(10,9) = 18
f(10,10) = 1

f(11,1) = 1
f(11,2) = 7477161
f(11,3) = 21993884
f(11,4) = 8457285
f(11,5) = 1695429
f(11,6) = 257400
f(11,7) = 32010
f(11,8) = 3322
f(11,9) = 287
f(11,10) = 20
f(11,11) = 1

f(12,1) = 1
f(12,2) = 74207208
f(12,3) = 266361634
f(12,4) = 111323149
f(12,5) = 23023811
f(12,6) = 3574957
f(12,7) = 456720
f(12,8) = 49236
f(12,9) = 4512
f(12,10) = 349
f(12,11) = 22
f(12,12) = 1

f(13,1) = 1
f(13,2) = 797771520
f(13,3) = 3465832370
f(13,4) = 1569068565
f(13,5) = 333840443
f(13,6) = 52785901
f(13,7) = 6881160
f(13,8) = 761904
f(13,9) = 72540
f(13,10) = 5954
f(13,11) = 417
f(13,12) = 24
f(13,13) = 1

f(14,1) = 1
f(14,2) = 9236662345
f(14,3) = 48245601976
f(14,4) = 23592426102
f(14,5) = 5153118154
f(14,6) = 827242933
f(14,7) = 109546009
f(14,8) = 12372360
f(14,9) = 1209936
f(14,10) = 103194
f(14,11) = 7672
f(14,12) = 491
f(14,13) = 26
f(14,14) = 1

f(15,1) = 1
f(15,2) = 114579019468
f(15,3) = 715756932697
f(15,4) = 377105857043
f(15,5) = 84426592621
f(15,6) = 13730434111
f(15,7) = 1841298059
f(15,8) = 211170960
f(15,9) = 21064680
f(15,10) = 1845480
f(15,11) = 142590
f(15,12) = 9690
f(15,13) = 571
f(15,14) = 28
f(15,15) = 1

f(16,1) = 1
f(16,2) = 1516103040832
f(16,3) = 11277786883720
f(16,4) = 6387313185576
f(16,5) = 1463941342191
f(16,6) = 240806565782
f(16,7) = 32629877967
f(16,8) = 3788091451
f(16,9) = 383685120
f(16,10) = 34288800
f(16,11) = 2721600
f(16,12) = 192240
f(16,13) = 12032
f(16,14) = 657
f(16,15) = 30
f(16,16) = 1

f(17,1) = 1
f(17,2) = 21314681315997
f(17,3) = 188135296651083
f(17,4) = 114303481217657
f(17,5) = 26793750988542
f(17,6) = 4452251786946
f(17,7) = 608572228291
f(17,8) = 71356438043
f(17,9) = 7315701120
f(17,10) = 663848640
f(17,11) = 53749920
f(17,12) = 3900480
f(17,13) = 253776
f(17,14) = 14722
f(17,15) = 749
f(17,16) = 32
f(17,17) = 1

f(18,1) = 1
f(18,2) = 317288088082404
f(18,3) = 3313338641692957
f(18,4) = 2155348564847332
f(18,5) = 516319125748337
f(18,6) = 86585391630673
f(18,7) = 11923667699474
f(18,8) = 1409672722481
f(18,9) = 145957544981
f(18,10) = 13406178240
f(18,11) = 1102187520
f(18,12) = 81591840
f(18,13) = 5454144
f(18,14) = 328950
f(18,15) = 17784
f(18,16) = 847
f(18,17) = 34
f(18,18) = 1

f(19,1) = 1
f(19,2) = 4985505271920096
f(19,3) = 61444453534759589
f(19,4) = 42719058006864690
f(19,5) = 10451197169218523
f(19,6) = 1767406549387381
f(19,7) = 244964063143590
f(19,8) = 29163603260677
f(19,9) = 3044416187213
f(19,10) = 282398538240
f(19,11) = 23500653120
f(19,12) = 1766525760
f(19,13) = 120466080
f(19,14) = 7465176
f(19,15) = 419634
f(19,16) = 21242
f(19,17) = 951
f(19,18) = 36
f(19,19) = 1

f(20,1) = 1
f(20,2) = 82459612672301845
f(20,3) = 1196988740015236617
f(20,4) = 887953677898186108
f(20,5) = 221738082618710329
f(20,6) = 37790452850585180
f(20,7) = 5267496652725480
f(20,8) = 630867328411136
f(20,9) = 66312765615259
f(20,10) = 6201593613645
f(20,11) = 521194867200
f(20,12) = 39656131200
f(20,13) = 2746068480
f(20,14) = 173606040
f(20,15) = 10027440
f(20,16) = 527820
f(20,17) = 25120
f(20,18) = 1061
f(20,19) = 38
f(20,20) = 1


EIS sequence A064315

f(n,k) = number of permutations of {1,...,n} whose shortest run of
increasing adjacent elements is of length k.

f(1,1) = 1

f(2,1) = 1
f(2,2) = 1

f(3,1) = 5
f(3,2) = 0
f(3,3) = 1

f(4,1) = 18
f(4,2) = 5
f(4,3) = 0
f(4,4) = 1

f(5,1) = 101
f(5,2) = 18
f(5,3) = 0
f(5,4) = 0
f(5,5) = 1

f(6,1) = 611
f(6,2) = 89
f(6,3) = 19
f(6,4) = 0
f(6,5) = 0
f(6,6) = 1

f(7,1) = 4452
f(7,2) = 519
f(7,3) = 68
f(7,4) = 0
f(7,5) = 0
f(7,6) = 0
f(7,7) = 1

f(8,1) = 36287
f(8,2) = 3853
f(8,3) = 110
f(8,4) = 69
f(8,5) = 0
f(8,6) = 0
f(8,7) = 0
f(8,8) = 1

f(9,1) = 333395
f(9,2) = 27555
f(9,3) = 1679
f(9,4) = 250
f(9,5) = 0
f(9,6) = 0
f(9,7) = 0
f(9,8) = 0
f(9,9) = 1

f(10,1) = 3382758
f(10,2) = 233431
f(10,3) = 11941
f(10,4) = 418
f(10,5) = 251
f(10,6) = 0
f(10,7) = 0
f(10,8) = 0
f(10,9) = 0
f(10,10) = 1

f(11,1) = 37688597
f(11,2) = 2167152
f(11,3) = 59470
f(11,4) = 658
f(11,5) = 922
f(11,6) = 0
f(11,7) = 0
f(11,8) = 0
f(11,9) = 0
f(11,10) = 0
f(11,11) = 1

f(12,1) = 456839351
f(12,2) = 21596120
f(12,3) = 528974
f(12,4) = 34649
f(12,5) = 1582
f(12,6) = 923
f(12,7) = 0
f(12,8) = 0
f(12,9) = 0
f(12,10) = 0
f(12,11) = 0
f(12,12) = 1

f(13,1) = 5989023768
f(13,2) = 232817282
f(13,3) = 4907480
f(13,4) = 266267
f(13,5) = 2572
f(13,6) = 3430
f(13,7) = 0
f(13,8) = 0
f(13,9) = 0
f(13,10) = 0
f(13,11) = 0
f(13,12) = 0
f(13,13) = 1

f(14,1) = 84421235807
f(14,2) = 2718706924
f(14,3) = 36965659
f(14,4) = 1369372
f(14,5) = 4002
f(14,6) = 6004
f(14,7) = 3431
f(14,8) = 0
f(14,9) = 0
f(14,10) = 0
f(14,11) = 0
f(14,12) = 0
f(14,13) = 0
f(14,14) = 1

f(15,1) = 1273482972215
f(15,2) = 33814848445
f(15,3) = 370685663
f(15,4) = 5082045
f(15,5) = 756755
f(15,6) = 10008
f(15,7) = 12868
f(15,8) = 0
f(15,9) = 0
f(15,10) = 0
f(15,11) = 0
f(15,12) = 0
f(15,13) = 0
f(15,14) = 0
f(15,15) = 1

f(16,1) = 20470309460322
f(16,2) = 448311181346
f(16,3) = 4086527638
f(16,4) = 76637635
f(16,5) = 6029297
f(16,6) = 16014
f(16,7) = 22878
f(16,8) = 12869
f(16,9) = 0
f(16,10) = 0
f(16,11) = 0
f(16,12) = 0
f(16,13) = 0
f(16,14) = 0
f(16,15) = 0
f(16,16) = 1

f(17,1) = 349326503482301
f(17,2) = 6319365554730
f(17,3) = 40650345653
f(17,4) = 876858377
f(17,5) = 31742676
f(17,6) = 24750
f(17,7) = 38894
f(17,8) = 48618
f(17,9) = 0
f(17,10) = 0
f(17,11) = 0
f(17,12) = 0
f(17,13) = 0
f(17,14) = 0
f(17,15) = 0
f(17,16) = 0
f(17,17) = 1

f(18,1) = 6307682420743595
f(18,2) = 94225534689624
f(18,3) = 458464525689
f(18,4) = 7147459470
f(18,5) = 120956707
f(18,6) = 17153135
f(18,7) = 63646
f(18,8) = 87514
f(18,9) = 48619
f(18,10) = 0
f(18,11) = 0
f(18,12) = 0
f(18,13) = 0
f(18,14) = 0
f(18,15) = 0
f(18,16) = 0
f(18,17) = 0
f(18,18) = 1

f(19,1) = 120157254334350828
f(19,2) = 1481940898130323
f(19,3) = 5857242113368
f(19,4) = 47396097511
f(19,5) = 398182782
f(19,6) = 139520497
f(19,7) = 100774
f(19,8) = 151162
f(19,9) = 184754
f(19,10) = 0
f(19,11) = 0
f(19,12) = 0
f(19,13) = 0
f(19,14) = 0
f(19,15) = 0
f(19,16) = 0
f(19,17) = 0
f(19,18) = 0
f(19,19) = 1

f(20,1) = 2408293016265606623
f(20,2) = 24536143182460549
f(20,3) = 72283039099029
f(20,4) = 552146011437
f(20,5) = 12794989968
f(20,6) = 747544744
f(20,7) = 155038
f(20,8) = 251938
f(20,9) = 335918
f(20,10) = 184755
f(20,11) = 0
f(20,12) = 0
f(20,13) = 0
f(20,14) = 0
f(20,15) = 0
f(20,16) = 0
f(20,17) = 0
f(20,18) = 0
f(20,19) = 0
f(20,20) = 1