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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.
7
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
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
KEYWORD
nonn,tabl,easy
AUTHOR
Henry Bottomley, Apr 02 2001
STATUS
approved