cp's OEIS Frontend

A066991 Square array read by descending antidiagonals of number of ways of dividing n*k labeled items into k unlabeled orders with n items in each order.

%I A066991 #13 Feb 19 2024 04:35:49
%S A066991 1,1,2,1,12,6,1,120,360,24,1,1680,60480,20160,120,1,30240,19958400,
%T A066991 79833600,1814400,720,1,665280,10897286400,871782912000,217945728000,
%U A066991 239500800,5040,1,17297280,8892185702400,20274183401472000
%N A066991 Square array read by descending antidiagonals of number of ways of dividing n*k labeled items into k unlabeled orders with n items in each order.
%C A066991 T(p,k) = (pk)!/k! is divisible by p^k but not p^(k+1) for p prime; e.g., T(3,4) = 3^4*11*10*8*7*5*4*2*1 = 19958400.
%H A066991 Paolo Xausa, <a href="/A066991/b066991.txt">Table of n, a(n) for n = 1..820</a> (antidiagonals 1..40 of the array, flattened).
%F A066991 T(n,k) = (n*k)!/k!.
%e A066991 The array begins:
%e A066991   n\k|   1        2             3                   4  ...
%e A066991   --------------------------------------------------------
%e A066991    1 |   1,       1,            1,                  1, ...
%e A066991    2 |   2,      12,          120,               1680, ...
%e A066991    3 |   6,     360,        60480,           19958400, ...
%e A066991    4 |  24,   20160,     79833600,       871782912000, ...
%e A066991    5 | 120, 1814400, 217945728000, 101370917007360000, ...
%e A066991   ...
%t A066991 Table[((n-k+1)*k)!/k!, {n, 10}, {k, n, 1, -1}] (* _Paolo Xausa_, Feb 19 2024 *)
%Y A066991 Rows include A000012, A001813, A064350.
%Y A066991 Columns include A000142, A002674, A065961.
%Y A066991 Cf. A060538, A060539, A060540.
%K A066991 nonn,tabl
%O A066991 1,3
%A A066991 _Henry Bottomley_, Feb 01 2002
%E A066991 Edited by _Paolo Xausa_, Feb 19 2024