W. Lang, Sep 17 2008 A144274 tabf array: partition numbers M32hat(-2)= 'M32(-2)/M3'. 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 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 80 10 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 880 80 20 10 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 12320 880 160 100 80 20 8 10 4 2 1 0 0 0 0 0 0 0 0 0 0 0 7 209440 12320 1760 800 880 160 100 40 80 20 8 10 4 2 1 0 0 0 0 0 0 0 8 4188800 209440 24640 8800 6400 12320 1760 800 320 200 880 160 100 40 16 80 20 8 10 4 2 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 .. n=9: [96342400, 4188800, 418880, 123200, 70400, 209440, 24640, 8800, 6400, 3520, 1600, 1000, 12320, 1760, 800, 320, 200, 80, 880, 160, 100, 40, 16, 80, 20, 8, 10, 4, 2, 1], n=10:[2504902400, 96342400, 8377600, 2094400, 985600, 774400, 4188800, 418880, 123200, 70400, 49280, 17600, 12800, 8000, 209440, 24640, 8800, 6400, 3520, 1600, 1000, 640, 400, 12320, 1760, 800, 320, 200, 80, 32, 880, 160, 100, 40, 16, 80, 20, 8, 10, 4, 2, 1]. The first column gives A008544(n-1)=(3*n-4)(!^3),n>=2, (3-factorials) and 1 for n=1. The row sums give for n>=1: A144276=[1,3,13,97,997,13585,225625,4454801,101415881,2618639033,...]. They coincide with the row sums of triangle S2hat(-2)= A144275. ########################################### e.o.f. ############################################################################################################################