W. Lang, Sep 16 2008 A143171 tabf array: partition numbers M32(-1). 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 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 15 12 3 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 105 75 30 30 15 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 945 630 225 90 225 180 15 60 45 15 1 0 0 0 0 0 0 0 0 0 0 0 7 10395 6615 2205 1575 2205 1575 630 315 525 630 105 105 105 21 1 0 0 0 0 0 0 0 8 135135 83160 26460 17640 7875 26460 17640 12600 3150 2520 5880 6300 2520 2520 105 1050 1680 420 168 210 28 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: [2027025, 1216215, 374220, 238140, 198450, 374220, 238140, 158760, 70875, 39690, 56700, 7560, 79380, 79380, 56700, 28350, 22680, 3780, 13230, 18900, 7560, 11340, 945, 1890, 3780, 1260, 252, 378, 36, 1], n=10: [34459425, 20270250, 6081075, 3742200, 2976750, 1389150, 6081075, 3742200, 2381400, 1984500, 595350, 793800, 354375, 283500, 1247400, 1190700, 793800, 354375, 396900, 567000, 75600, 47250, 56700, 198450, 264600, 189000, 141750, 113400, 37800, 945, 26460, 47250, 18900, 37800, 4725, 3150, 7560, 3150, 360, 630, 45, 1]. The first column gives A001147(n-1)=(2*n-3)(!^2),n>=2, (2-factorials) and 1 for n=1. The row sums give, for n>=1: A001515(n)=[1,2,7,37,266,2431,27007,353522,5329837,90960751,...]. They coincide with the row sums of triangle A001497. ########################################### e.o.f. ############################################################################################################################