W. Lang Sep 22 2008 A144356 tabf array: partition numbers M31(6). Partitions of n listed in Abramowitz-Stegun order p. 831-2 (see the main page for an A-number with the reference). n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ... 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 42 18 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 336 168 108 36 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3024 1680 2520 420 540 60 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 30240 18144 30240 17640 5040 15120 3240 840 1620 90 1 0 0 0 0 0 0 0 0 0 0 0 7 332640 211680 381024 493920 63504 211680 123480 158760 11760 52920 22680 1470 3780 126 1 0 0 0 0 0 0 0 8 3991680 2661120 5080320 7112448 3951360 846720 3048192 3951360 2540160 2963520 169344 846720 493920 1270080 136080 23520 141120 90720 2352 7560 168 1 . . . n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ... The next two rows, for n=9 and n=10, are: n=9: [51891840, 35925120, 71850240, 106686720, 128024064, 11975040, 45722880, 64012032, 35562240, 41150592, 106686720, 20744640, 2540160, 13716864, 17781120, 22861440, 26671680, 11430720, 381024, 2540160, 1481760, 5715360, 1224720, 42336, 317520, 272160, 3528, 13608, 216, 1]. n=10: [726485760, 518918400, 1077753600, 1676505600, 2133734400, 1152216576, 179625600, 718502400, 1066867200, 1280240640, 685843200, 1920360960, 1066867200, 1244678400, 39916800, 228614400, 320060160, 177811200, 411505920, 1066867200, 207446400, 228614400, 400075200, 6350400, 45722880, 59270400, 114307200, 133358400, 114307200, 7348320, 762048, 6350400, 3704400, 19051200, 6123600, 70560, 635040, 680400, 5040, 22680, 270, 1]. The row sums give, for n>=1: A049402 = [1,7,61,649,8245,122215,2069425,39328465,827226505,19047582055,...]. They coincide with the row sums of triangle A049374. ########################################### e.o.f. #####################################################################################