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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-Fran├žois 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 February 16 21:26 EST 2020. Contains 331975 sequences. (Running on oeis4.)