A189389 Number of permutations p of [n] such that (n-p(i)+i) mod n >= 5 for all i.

1, 0, 0, 0, 0, 0, 1, 2, 49, 484, 6208, 79118, 1081313, 15610304, 238518181, 3850864416, 65598500129, 1177003136892, 22203823852849, 439598257630414, 9117748844458320, 197776095898147080, 4479171132922158213, 105749311074795459594, 2598770324359627927649

Offset: 0

Author

Alois P. Heinz, Apr 20 2011

Keywords

• nonn

Examples

			a(7) = 2: (2,3,4,5,6,7,1), (3,4,5,6,7,1,2).
		

Links

• Shalosh B. Ekhad and Doron Zeilberger, Table of n, a(n) for n = 0..100
• D. Zeilberger, Automatic Enumeration of Generalized Ménage Numbers

Crossrefs

A diagonal of A008305.

Cf. A000142, A000166, A000179, A000183, A004307.

Programs

Maple

with(LinearAlgebra):
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)->
                     `if`(i-j<=0 and i-j>-5 or i-j>n-5, 0, 1)))):
seq(a(n), n=0..15);

Mathematica

a[n_] := Permanent[Table[If[i-j <= 0 && i-j > -5 || i-j > n-5, 0, 1], {i, 1, n}, {j, 1, n}]]; a[0] = 1; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jan 07 2016, adapted from Maple *)