W. Lang, Nov 09 2007 A134284 tabf array: partition numbers M_0(3)/M_0 = M0(3)/M0. 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 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 10 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 35 10 9 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 126 35 30 10 9 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 462 126 105 100 35 30 27 10 9 3 1 0 0 0 0 0 0 0 0 0 0 0 7 1716 462 378 350 126 105 100 90 35 30 27 10 9 3 1 0 0 0 0 0 0 0 8 6435 1716 1386 1260 1225 462 378 350 315 300 126 105 100 90 81 35 30 27 10 9 3 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: [24310, 6435, 5148, 4620, 4410, 1716, 1386, 1260, 1225, 1134, 1050, 1000, 462, 378, 350, 315, 300, 270, 126, 105, 100, 90, 81, 35, 30, 27, 10, 9, 3, 1]. n=10:[92378, 24310, 19305, 17160, 16170, 15876, 6435, 5148, 4620, 4410, 4158, 3780, 3675, 3500, 1716, 1386, 1260, 1225, 1134, 1050, 1000, 945, 900, 462, 378, 350, 315, 300, 270, 243, 126, 105, 100, 90, 81, 35, 30, 27, 10, 9, 3, 1]. The first column gives A001700(n-1), n>=1: [1,3,10,35,126,462,1716,6435,24310,92378,...]. The row sums give, for n>=1: A134826= 1,4,14,58,214,908,3442,14444,56386,234476,920490,3847998,15165982,...]. They coincide with the row sums of triangle A134285. ########################################### e.o.f. ############################################################################################################################