W. Lang Sep 22 2008 A144355 tabf array: partition numbers M31(5). 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 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 30 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 210 120 75 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1680 1050 1500 300 375 50 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 15120 10080 15750 9000 3150 9000 1875 600 1125 75 1 0 0 0 0 0 0 0 0 0 0 0 7 151200 105840 176400 220500 35280 110250 63000 78750 7350 31500 13125 1050 2625 105 1 0 0 0 0 0 0 0 8 1663200 120960 211680 2822400 1543500 423360 1411200 1764000 1102500 1260000 94080 441000 252000 630000 65625 14700 84000 52500 1680 5250 140 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: [19958400, 14968800, 27216000, 38102400, 44452800, 5443200, 19051200, 25401600, 13891500, 15876000, 39690000, 7560000, 1270080, 6350400, 7938000, 9922500, 11340000, 4725000, 211680, 1323000, 756000, 2835000, 590625, 26460, 189000, 157500, 2520, 9450, 180, 1], n=10: [259459200, 199584000, 374220000, 544320000, 666792000, 355622400, 74844000, 272160000, 381024000, 444528000, 238140000, 635040000, 347287500, 396900000, 18144000, 95256000, 127008000, 69457500, 158760000, 396900000, 75600000, 82687500, 141750000, 3175200, 21168000, 26460000, 49612500, 56700000, 47250000, 2953125, 423360, 3307500, 1890000, 9450000, 2953125, 44100, 378000, 393750, 3600, 15750, 225, 1]. The row sums give, for n>=1: A049378 = [1,6,46,436,4956,65776,996976,16957536,319259296,6581662336,...]. They coincide with the row sums of triangle A049353. ########################################### e.o.f. #####################################################################################