A100246 Number of permutations of {1,2,3,...,n^2} where no multiples of n are consecutive.

1, 12, 151200, 8219667456000, 5940854755726373683200000, 140616461430273488287535887653273600000000, 228186389638197777421971812759876473627903014249431040000000000

Offset

1,2

Comments

limit{n->oo} a(n)/(n^2)! = 1/e.

Links

Table of n, a(n) for n=1..7.

Formula

a(n) = (n^2 -n)! *(n^2 -n +1)! /(n^2 -2*n +1)!.

Example

If n = 2, we have the permutations:
1,2,3,4; 1,4,3,2; 3,2,1,4; 3,4,1,2;
2,1,3,4; 4,1,3,2; 2,3,1,4; 4,3,1,2;
2,1,4,3; 4,1,2,3; 2,3,4,1; 4,3,2,1
(no multiples of 2 are adjacent in any of the permutations). So a(2) = 12.

Maple

a:=n->(n^2-n)!*(n^2-n+1)!/(n^2-2*n +1)!: seq(a(n), n=1..8); # Emeric Deutsch, Aug 03 2005

Crossrefs

Sequence in context: A328992 A069048 A284287 * A055323 A368686 A333099

Adjacent sequences: A100243 A100244 A100245 * A100247 A100248 A100249

Keyword

nonn

Author

Leroy Quet, Jan 11 2005

Extensions

More terms from Emeric Deutsch, Aug 03 2005

Status

approved