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

0,3

Links

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

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).

Example

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

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 *)

Crossrefs

Cf. A000166, A007318, A008290, A098825.

Sequence in context: A204563 A356540 A196449 * A186196 A196478 A001367

Adjacent sequences: A281259 A281260 A281261 * A281263 A281264 A281265

Keyword

nonn

Author

Alois P. Heinz, Apr 12 2017

Status

approved