%I #26 Sep 08 2022 08:45:50

%S 1,1,12870,9465511770,99561092450391000,7656714453153197981835000,

%T 2889253496242619386328267523990000,

%U 4104167472585675600759440022842715359250000,18165723931630806756964027928179555634194028454000000

%N a(n) = (8n)!/(8!^n).

%C From _Tilman Piesk_, Oct 30 2014: (Start)

%C Column 8 of A187783.

%C Number of permutations of a multiset that contains n different elements, each occurring 8 times.

%C Or in other words (the former title of this sequence):

%C Number of 8*n X n 0..1 arrays with row sums 1 and column sums 8.

%C (End)

%H Tilman Piesk, <a href="/A172609/b172609.txt">Table of n, a(n) for n = 0..54</a> (first 12 terms from R. H. Hardin)

%F a(n) = (8n)!/(8!^n).

%e a(3) = (8*3)!/(8!^3) = 9465511770 is the number of permutations of a multiset that contains 3 different elements 8 times, e.g., {1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3}.

%p A172609:=n->(8*n)!/(40320^n): seq(A172609(n), n=0..10); # _Wesley Ivan Hurt_, Nov 01 2014

%t Table[(8 n)! / (40320^n), {n, 0, 10}] (* _Vincenzo Librandi_, Nov 01 2014 *)

%o (Magma) [Factorial(8*n)/(40320^n): n in [0..20]]; // _Vincenzo Librandi_, Nov 01 2014

%K nonn,easy

%O 0,3

%A _R. H. Hardin_, Feb 06 2010

%E Name changed by _Tilman Piesk_, Oct 30 2014