W. Lang, Nov 09 2007 A134274 tabf array: partition numbers M_3(5)/M_3= M3(5)/M3. 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 45 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 585 45 25 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 9945 585 225 45 25 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 208845 9945 2925 2025 585 225 125 45 25 5 1 0 0 0 0 0 0 0 0 0 0 0 7 5221125 208845 49725 26325 9945 2925 2025 1125 585 225 125 45 25 5 1 0 0 0 0 0 0 0 8 151412625 5221125 1044225 447525 342225 208845 49725 26325 14625 10125 9945 2925 2025 1125 625 585 225 125 45 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: [4996616625, 151412625, 26105625, 9398025, 5817825, 5221125, 1044225, 447525, 342225, 248625, 131625, 91125, 208845, 49725, 26325, 14625, 10125, 5625, 9945, 2925, 2025, 1125, 625, 585, 225, 125, 45, 25, 5, 1], n=10: [184874815125, 4996616625, 757063125, 234950625, 122174325, 98903025, 151412625, 26105625, 9398025, 5817825, 5221125, 2237625, 1711125, 1184625, 5221125, 1044225, 447525, 342225, 248625, 131625, 91125, 73125, 50625, 208845, 49725, 26325, 14625, 10125, 5625, 3125, 9945, 2925, 2025, 1125, 625, 585, 225, 125, 45, 25, 5, 1]. The first column gives A007696(n) = S2(5,n,1) = [1,5,45,585,9945,208845,5221125,151412625,4996616625,184874815125,...]. The row sums give, for n>=1: A134276 = [1,6,51,661,10831,224751,5523051,158795026,5197210126,191295597726,...], and coincide with those of triangle A134275. ########################################### e.o.f. #####################################################################################