W. Lang Oct 10 2008 A145372 tabf array: partition numbers M31hat(-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 20 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 60 20 25 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 120 60 100 20 25 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 120 120 300 400 60 100 125 20 25 5 1 0 0 0 0 0 0 0 0 0 0 0 7 0 120 600 1200 120 300 400 500 60 100 125 20 25 5 1 0 0 0 0 0 0 0 8 0 0 600 2400 3600 120 600 1200 1500 2000 120 300 400 500 625 60 100 125 20 25 5 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, 2400, 7200, 0, 600, 2400, 3600, 3000, 6000, 8000, 120, 600, 1200, 1500, 2000, 2500, 120, 300, 400, 500, 625, 60, 100, 125, 20, 25, 5, 1], n=10: [0, 0, 0, 0, 7200, 14400, 0, 0, 2400, 7200, 3000, 12000, 18000, 24000, 0, 600, 2400, 3600, 3000, 6000, 8000, 7500, 10000, 120, 600, 1200, 1500, 2000, 2500, 3125, 120, 300, 400, 500, 625, 60, 100, 125, 20, 25, 5, 1]. The row sums give, for n>=1, A145374 : [1,6,26,111,331,1276,3576,14301,43401,142626,...]. They coincide with the row sums of triangle A145373 = S1hat(-5). ########################################### e.o.f. #####################################################################################