W. Lang, Sep 16 2008 A143172 tabf array: partition numbers M32(-2). Row n is filled with zeros for k>p(n), the partition number. 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 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 10 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 80 40 12 12 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 880 400 200 100 60 20 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 12320 5280 2400 1000 1200 1200 120 200 180 30 1 0 0 0 0 0 0 0 0 0 0 0 7 209440 86240 36960 28000 18480 16800 7000 4200 2800 4200 840 350 420 42 1 0 0 0 0 0 0 0 8 4188800 1675520 689920 492800 224000 344960 295680 224000 67200 56000 49280 67200 28000 33600 1680 5600 11200 3360 560 840 56 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: [96342400, 37699200, 15079680, 10348800, 8870400, 7539840, 6209280, 4435200, 2016000, 1330560, 2016000, 280000, 1034880, 1330560, 1008000, 604800, 504000, 100800, 110880, 201600, 84000, 151200, 15120, 10080, 25200, 10080, 840, 1512, 72, 1], n=10: [2504902400, 963424000, 376992000, 251328000, 206976000, 97574400, 188496000, 150796800, 103488000, 88704000, 31046400, 44352000, 20160000, 16800000, 25132800, 31046400, 22176000, 10080000, 13305600, 20160000, 2800000, 2016000, 2520000, 2587200, 4435200, 3360000, 3024000, 2520000, 1008000, 30240, 221760, 504000, 210000, 504000, 75600, 16800, 50400, 25200, 1200, 2520, 90, 1]. The first column gives A008544(n-1)=(3*n-4)(!^3),n>=2, (3-factorials) and 1 for n=1: [1, 2, 10, 80, 880, 12320, 209440, 4188800, 96342400,...]. The row sums give, for n>=1: A015735 = [1,3,17,145,1661,23931,415773,8460257,197360985,5192853011,...]. They coincide with the row sums of triangle A004747. ########################################### e.o.f. ############################################################################################################################