A275064 Number of permutations p of [n] such that p(i)-i is a multiple of nine for all i in [n].

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1536, 4608, 13824, 41472, 124416, 373248, 1119744, 3359232, 10077696, 40310784, 161243136, 644972544, 2579890176, 10319560704, 41278242816, 165112971264, 660451885056, 2641807540224

Offset: 0

Author

Alois P. Heinz, Jul 15 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..683

Crossrefs

Column k=9 of A275062.

Programs

Mathematica

Table[Product[Floor[(n + i)/9]!, {i, 0, 8}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 02 2018 *)

Formula

a(n) = Product_{i=0..8} floor((n+i)/9)!.

a(n) ~ (2*Pi*n)^4 * n! / 9^(n + 9/2). - Vaclav Kotesovec, Oct 02 2018