A216778 Number of derangements on n elements with an even number of cycles.

1, 0, 0, 0, 3, 20, 130, 924, 7413, 66744, 667476, 7342280, 88107415, 1145396460, 16035550518, 240533257860, 3848532125865, 65425046139824, 1177650830516968, 22375365779822544, 447507315596451051, 9397653627525472260, 206748379805560389930, 4755212735527888968620

Offset

0,5

Links

Michael De Vlieger, Table of n, a(n) for n = 0..450

Paulo H. L. Martins, Ronald Dickman, and Robert M. Ziff, Percolation in two-species antagonistic random sequential adsorption in two dimensions, arXiv:2211.04622 [cond-mat.stat-mech], 2022.

Formula

a(n+1) = n*(a(n) + a(n-1) + n - 2), a(0)=1, a(1)=0.

a(n) = (A000166(n) - n + 1)/2.

E.g.f.: cosh(log(1/(1-x)) - x). - Geoffrey Critzer, Jun 23 2014

Maple

a := proc (n) local x, y, t, k; if n = 0 then 1 elif n = 1 then 0 else x := 1; y := 0; for k from 2 to n do t := y; y := (k-1)*(x+y+k-3); x := t end do; y end if end proc;

Mathematica

nn=23; Range[0, nn]!*CoefficientList[Series[Cosh[Log[1/(1-x)]-x], {x, 0, nn}], x] (* Geoffrey Critzer, Jun 23 2014 *)

Crossrefs

Cf. A000166, A216779 (derangements with odd number of cycles).

Sequence in context: A228884 A138910 A000276 * A337105 A056306 A056298

Adjacent sequences: A216775 A216776 A216777 * A216779 A216780 A216781

Keyword

nonn,easy

Author

José H. Nieto S., Sep 16 2012

Status

approved