A060538 Square array read by antidiagonals of number of ways of dividing n*k labeled items into n labeled boxes with k items in each box.

1, 1, 2, 1, 6, 6, 1, 20, 90, 24, 1, 70, 1680, 2520, 120, 1, 252, 34650, 369600, 113400, 720, 1, 924, 756756, 63063000, 168168000, 7484400, 5040, 1, 3432, 17153136, 11732745024, 305540235000, 137225088000, 681080400, 40320, 1, 12870

Offset

1,3

Links

Harry J. Smith, Table of n, a(n) for n = 1..210

Formula

T(n, k) = (nk)!/k!^n = T(n-1, k)*binomial(nk, k) = T(n-1, k)*A060539(n, k) = A060540(n, k)*A000142(k).

Example

       1        1        1        1
       2        6       20       70
       6       90     1680    34650
      24     2520   369600 63063000

Prog

(PARI) T(n, k)=(n*k)!/k!^n;
for(n=1, 6, for(k=1, 6, print1(T(n, k), ", ")); print) \\ Harry J. Smith, Jul 06 2009

Crossrefs

Subtable of A187783.

Rows include A000012, A000984, A006480, A008977, A008978 etc.

Columns include A000142, A000680, A014606, A014608, A014609 etc.

Main diagonal is A034841.

Sequence in context: A300700 A046521 A104684 * A260848 A110183 A110098

Adjacent sequences: A060535 A060536 A060537 * A060539 A060540 A060541

Keyword

nonn,tabl,easy

Author

Henry Bottomley, Apr 02 2001

Status

approved