A281262 Number of permutations of [2n] with exactly n fixed points.

1, 0, 6, 40, 630, 11088, 244860, 6362928, 190900710, 6490575520, 246642054516, 10358965584240, 476512419579196, 23825620968559200, 1286583532342313400, 74621844875699059680, 4626554382293942780550, 305352589231397889910080, 21374681246197861368840900

Offset: 0

Author

Alois P. Heinz, Apr 12 2017

Keywords

• nonn

Examples

			a(2) = 6: 1243, 1324, 1432, 2134, 3214, 4231.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..366

Crossrefs

Cf. A000166, A007318, A008290, A098825.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 1-n,
      (4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n)
    end:
seq(a(n), n=0..20);

Mathematica

a[n_] := Binomial[2n, n] Subfactorial[n];
a /@ Range[0, 20] (* Jean-François Alcover, Sep 01 2021 *)

Formula

a(n) = (4*n-2)*((n-1)*a(n-1)+(4*n-6)*a(n-2))/n for n>1, a(n) = 1-n for n<2.

a(n) = binomial(2n,n) * A000166(n).

a(n) = A008290(2n,n) = A098825(2n,n).