W. Lang, Nov 09 2007 A134144 tabf array: partition numbers M_3(3)= M3(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 15 9 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 105 60 27 18 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 945 525 450 150 135 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 10395 5670 4725 2250 1575 2700 405 300 405 45 1 0 0 0 0 0 0 0 0 0 0 0 7 135135 72765 59535 55125 19845 33075 15750 14175 3675 9450 2835 525 945 63 1 0 0 0 0 0 0 0 8 2027025 1081080 873180 793800 385875 291060 476280 441000 198450 189000 52920 132300 63000 113400 8505 7350 25200 11340 840 1890 84 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: [34459425, 18243225, 14594580, 13097700, 12502350, 4864860, 7858620, 7144200, 3472875, 3214890, 5953500, 945000, 873180, 2143260, 1984500, 1786050, 1701000, 510300, 119070, 396900, 189000, 510300, 76545, 13230, 56700, 34020, 1260, 3402, 108, 1]. n=10: [654729075, 344594250, 273648375, 243243000, 229209750, 112521150, 91216125, 145945800, 130977000, 125023500, 58939650, 107163000, 52093125, 49612500, 16216200, 39293100, 35721000, 17364375, 32148900, 59535000, 9450000, 8930250, 12757500, 2182950, 7144200, 6615000, 8930250, 8505000, 5103000, 229635, 238140, 992250, 472500, 1701000, 382725, 22050, 113400, 85050, 1800, 5670, 135, 1] The row sums give, for n>=1: A049118= [1,4,25,211,2236,28471,422899,7173580,136750051,2893057381,...]. They coincide with the row sums of triangle A035342. ########################################### e.o.f. #####################################################################################