A333804 (1/16) times the number of permutations p of [n+2] such that |p(i+n) - p(i)| <> n for i in {1,2}.

0, 0, 1, 5, 34, 258, 2172, 20220, 207000, 2315880, 28143360, 369411840, 5210956800, 78636096000, 1264324723200, 21579740582400, 389730550809600, 7425628898688000, 148865650053120000, 3132539179241472000, 69036795668865024000, 1590266397644660736000

Offset: 0

Author

Alois P. Heinz, Apr 05 2020

Keywords

• nonn

Examples

			a(2) = 1: there are 16 permutations p of [4] such that |p(i+2) - p(i)| <> 2 for i in {1,2}: 1243, 1324, 1342, 1423, 2134, 2314, 2413, 2431, 3124, 3142, 3241, 3421, 4132, 4213, 4231, 4312.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..448
• Wikipedia, Permutation

Crossrefs

Cf. A333706.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, (n-1)*n/2, a(n-1)*
     (n-2)*(n^4+2*n^3-9*n^2+6*n+8)/(n^4-2*n^3-9*n^2+26*n-8))
    end:
seq(a(n), n=0..23);

Formula

E.g.f.: 1/(2*x-2)-1/(8*(x-1)^3)+log(1-x)*(1-x)/2+(5*x+3)/8.

a(n) = A333706(n+2,n)/16.