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 A060540 Square array read by antidiagonals downwards: T(n,k) = (n*k)!/(k!^n*n!), (n>=1, k>=1), the number of ways of dividing nk labeled items into n unlabeled boxes with k items in each box. 18
 1, 1, 1, 1, 3, 1, 1, 10, 15, 1, 1, 35, 280, 105, 1, 1, 126, 5775, 15400, 945, 1, 1, 462, 126126, 2627625, 1401400, 10395, 1, 1, 1716, 2858856, 488864376, 2546168625, 190590400, 135135, 1, 1, 6435, 66512160, 96197645544, 5194672859376, 4509264634875, 36212176000, 2027025, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Seiichi Manyama, Antidiagonals n = 1..50, flattened (first 20 antidiagonals from Harry J. Smith) FORMULA T(n,k) = (n*k)!/(k!^n*n!) = T(n-1,k)*A060543(n,k) = A060538(n,k)/A000142(k). T(n,k) = Product_{j=2,n} C(j*k-1,k-1). - M. F. Hasler, Aug 22 2014 EXAMPLE Array begins: 1,   1,       1,          1,             1,                 1, ... 1,   3,      10,         35,           126,               462, ... 1,  15,     280,       5775,        126126,           2858856, ... 1, 105,   15400,    2627625,     488864376,       96197645544, ... 1, 945, 1401400, 2546168625, 5194672859376, 11423951396577720, ... ... MATHEMATICA T[n_, k_] := (n*k)!/(k!^n*n!); Table[T[n-k+1, k], {n, 1, 10}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jun 29 2018 *) PROG (PARI) { i=0; for (m=1, 20, for (n=1, m, k=m - n + 1; write("b060540.txt", i++, " ", (n*k)!/(k!^n*n!))); ) } \\ Harry J. Smith, Jul 06 2009 CROSSREFS Rows include A000012, A001700, A060542, A082368, A322252. Columns k=1..10 give A000012, A001147, A025035, A025036, A025037, A025038, A025040, A025041, A025042. Main diagonal is A057599. Related to A057599, see also A096126 and A246048. Cf. A060358, A000142. Sequence in context: A176157 A176156 A172339 * A087647 A100265 A086766 Adjacent sequences:  A060537 A060538 A060539 * A060541 A060542 A060543 KEYWORD nonn,tabl AUTHOR Henry Bottomley, Apr 02 2001 EXTENSIONS Definition reworded by M. F. Hasler, Aug 23 2014 STATUS approved

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Last modified August 19 08:26 EDT 2019. Contains 326115 sequences. (Running on oeis4.)