cp's OEIS Frontend

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.

%I A060538 #18 Jul 03 2018 02:34:03
%S A060538 1,1,2,1,6,6,1,20,90,24,1,70,1680,2520,120,1,252,34650,369600,113400,
%T A060538 720,1,924,756756,63063000,168168000,7484400,5040,1,3432,17153136,
%U A060538 11732745024,305540235000,137225088000,681080400,40320,1,12870
%N 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.
%H A060538 Harry J. Smith, <a href="/A060538/b060538.txt">Table of n, a(n) for n = 1..210</a>
%F A060538 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).
%e A060538        1        1        1        1
%e A060538        2        6       20       70
%e A060538        6       90     1680    34650
%e A060538       24     2520   369600 63063000
%o A060538 (PARI) T(n,k)=(n*k)!/k!^n;
%o A060538 for(n=1, 6, for(k=1, 6, print1(T(n,k), ", ")); print) \\ _Harry J. Smith_, Jul 06 2009
%Y A060538 Subtable of A187783.
%Y A060538 Rows include A000012, A000984, A006480, A008977, A008978 etc.
%Y A060538 Columns include A000142, A000680, A014606, A014608, A014609 etc.
%Y A060538 Main diagonal is A034841.
%K A060538 nonn,tabl,easy
%O A060538 1,3
%A A060538 _Henry Bottomley_, Apr 02 2001