W. Lang, Nov 09 2007 A134149 tabf array: partition numbers M_3(4)= M3(4). 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 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 28 12 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 280 112 48 24 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3640 1400 1120 280 240 40 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 58240 21840 16800 7840 4200 6720 960 560 720 60 1 0 0 0 0 0 0 0 0 0 0 0 7 1106560 407680 305760 274400 76440 117600 54880 47040 9800 23520 6720 980 1680 84 1 0 0 0 0 0 0 0 8 24344320 8852480 6522880 5707520 2744000 1630720 2446080 2195200 940800 878080 203840 470400 219520 376320 26880 19600 62720 26880 1568 3360 112 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: [608608000, 219098880, 159344640, 136980480, 128419200, 39836160, 58705920, 51367680, 24696000, 22014720, 39513600, 6146560, 4892160, 11007360, 9878400, 8467200, 7902720, 2257920, 458640, 1411200, 658560, 1693440, 241920, 35280, 141120, 80640, 2352, 6048, 144, 1]. n=10: [17041024000, 6086080000, 4381977600, 3718041600, 3424512000, 1669449600, 1095494400, 1593446400, 1369804800, 1284192000, 587059200, 1027353600, 493920000, 460992000, 132787200, 293529600, 256838400, 123480000, 220147200, 395136000, 61465600, 56448000, 79027200, 12230400, 36691200, 32928000, 42336000, 39513600, 22579200, 967680, 917280, 3528000, 1646400, 5644800, 1209600, 58800, 282240, 201600, 3360, 10080, 180,1]. The first column gives A007559 = [1,4,28,280,3640,58240,1106560,24344320,608608000,17041024000,...], (3-factorials). The row sums give, for n>=1: A049119 = [1,5,41,465,6721,117941,2433145,57673281,1543866945,46052954821,...]. They coincide with the row sums of triangle A035469. ########################################### e.o.f. ############################################################################################################################