A172609 a(n) = (8n)!/(8!^n).

1, 1, 12870, 9465511770, 99561092450391000, 7656714453153197981835000, 2889253496242619386328267523990000, 4104167472585675600759440022842715359250000, 18165723931630806756964027928179555634194028454000000

Offset: 0

Author

R. H. Hardin, Feb 06 2010

Keywords

• nonn
• easy

Comments

From Tilman Piesk, Oct 30 2014: (Start)

Column 8 of A187783.

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

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

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

(End)

Examples

			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}.
		

Links

• Tilman Piesk, Table of n, a(n) for n = 0..54 (first 12 terms from R. H. Hardin)

Programs

Magma

[Factorial(8*n)/(40320^n):  n in [0..20]]; // Vincenzo Librandi, Nov 01 2014

Maple

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

Mathematica

Table[(8 n)! / (40320^n), {n, 0, 10}] (* Vincenzo Librandi, Nov 01 2014 *)

Formula

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

Extensions

Name changed by Tilman Piesk, Oct 30 2014