W. Lang Sep 22 2008 A144353 tabf array: partition numbers M31(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 12 9 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 60 48 27 18 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 360 300 360 120 135 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2520 2160 2700 1440 900 2160 405 240 405 45 1 0 0 0 0 0 0 0 0 0 0 0 7 20160 17640 22680 25200 7560 18900 10080 11340 2100 7560 2835 420 945 63 1 0 0 0 0 0 0 0 8 181440 161280 211680 241920 126000 70560 181440 201600 113400 120960 20160 75600 40320 90720 8505 4200 20160 11340 672 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 ... y The next two rows, for n=9 and n=10, are: n=9: [1814400, 1632960, 2177280, 2540160, 2721600, 725760, 1905120, 2177280, 1134000, 1224720, 2721600, 483840, 211680, 816480, 907200, 1020600, 1088640, 408240, 45360, 226800, 120960, 408240, 76545, 7560, 45360, 34020, 1008, 3402, 108, 1]. n=10: [19958400, 18144000, 24494400, 29030400, 31752000, 16329600, 8164800, 21772800, 25401600, 27216000, 14288400, 32659200, 17010000, 18144000, 2419200, 9525600, 10886400, 5670000, 12247200, 27216000, 4838400, 5103000, 8164800, 529200, 2721600, 3024000, 5103000, 5443200, 4082400, 229635, 90720, 567000, 302400, 1360800, 382725, 12600, 90720, 85050, 1440, 5670, 135, 1]. The row sums give, for n>=1: A049376=[1,4,22,154,1306,12976,147484,1883932,26680924,414468496,...]. They coincide with the row sums of triangle A046089. ########################################### e.o.f. #####################################################################################