A306675 Number of permutations p of [2n] having at least one index i with |p(i)-i| = n.

0, 1, 15, 455, 25487, 2293839, 302786759, 55107190151, 13225725636255, 4047072044694047, 1537887376983737879, 710503968166486900119, 392198190427900768865711, 254928823778135499762712175, 192726190776270437820610404327, 167671785975355280903931051764519

Offset: 0

Author

Alois P. Heinz, Mar 04 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..224
• Wikipedia, Permutation

Crossrefs

Cf. A306506, A306535.

Programs

Maple

b:= proc(n, k) b(n, k):= `if`(k=0, n!, b(n+1, k-1) -b(n, k-1)) end:
a:= n-> (2*n)! -b(0, 2*n):
seq(a(n), n=0..16);

Mathematica

b[n_, k_] := b[n, k] = If[k == 0, n!, b[n + 1, k - 1] - b[n, k - 1]];
a[n_] := (2n)! - b[0, 2n];
a /@ Range[0, 16] (* Jean-François Alcover, Apr 02 2021, after Alois P. Heinz *)

Formula

a(n) = A306506(2n,n).

a(n) = (2n)! - A306535(n).