W. Lang Sep 24 2008 A144358 tabf array: partition numbers M31(-2). 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 2 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 8 12 12 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 40 20 60 20 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 40 0 240 120 40 180 30 1 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 280 840 0 840 840 70 420 42 1 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2240 0 0 1120 6720 1680 0 2240 3360 112 840 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: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2240, 0, 0, 0, 0, 20160, 20160, 0, 0, 3360, 30240, 15120, 0, 5040, 10080, 168, 1512, 72, 1]. n=10: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22400, 0, 100800, 0, 0, 0, 0, 100800, 201600, 30240, 0, 0, 8400, 100800, 75600, 0, 10080, 25200, 240, 2520, 90, 1]. The row sums give, for n>=1: A049425 = [1,3,9,33,141,651,3333,18369,108153,678771,...]. They coincide with the row sums of triangle A049404 = S1(-2). ########################################### e.o.f. #####################################################################################