W. Lang, Nov 09 2007 A134283 tabf array: partition numbers M_0(3)= M0(3). 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 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 35 20 9 9 10 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 126 70 60 30 27 12 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 462 252 210 100 105 180 27 40 54 15 1 0 0 0 0 0 0 0 0 0 0 0 7 1716 924 756 700 378 630 300 270 140 360 108 50 90 18 1 0 0 0 0 0 0 0 8 6435 3432 2772 2520 1225 1386 2268 2100 945 900 504 1260 600 1080 81 175 600 270 60 135 21 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, 12870, 10296, 9240, 8820, 5148, 8316, 7560, 3675, 3402, 6300, 1000, 1848, 4536, 4200, 3780, 3600, 1080, 630, 2100, 1000, 2700, 405, 210, 900, 540, 70, 189, 24, 1]. n=10:[92378, 48620, 38610, 34320, 32340, 15876, 19305, 30888, 27720, 26460, 12474, 22680, 11025, 10500, 6864, 16632, 15120, 7350, 13608, 25200, 4000, 3780, 5400, 2310, 7560, 7000, 9450, 9000, 5400, 243, 756, 3150, 1500, 5400, 1215, 245, 1260, 945, 80, 252, 27, 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: A049027: [1,4,17,74,326,1446,6441,28770,128750,576944,...]. They coincide with the row sums of triangle A035324. ########################################### e.o.f. ############################################################################################################################