A275063 Number of permutations p of [n] such that p(i)-i is a multiple of eight for all i in [n].

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 768, 2304, 6912, 20736, 62208, 186624, 559872, 1679616, 6718464, 26873856, 107495424, 429981696, 1719926784, 6879707136, 27518828544, 110075314176, 550376570880, 2751882854400, 13759414272000

Offset: 0

Author

Alois P. Heinz, Jul 15 2016

Keywords

• nonn

Examples

			a(9) = 2: 123456789, 923456781.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..665

Crossrefs

Column k=8 of A275062.

Programs

Mathematica

Table[Product[Floor[(n + i)/8]!, {i, 0, 7}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 02 2018 *)

Formula

a(n) = Product_{i=0..7} floor((n+i)/8)!.

a(n) ~ (2*Pi*n)^(7/2) * n! / 8^(n + 4). - Vaclav Kotesovec, Oct 02 2018