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

Author

Henry Bottomley, Apr 02 2001

Keywords

• nonn
• tabl
• easy

Examples

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

Links

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

Crossrefs

Subtable of A187783.

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

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

Main diagonal is A034841.

Programs

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

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).