A216779 Number of derangements on n elements with an odd number of cycles.

0, 0, 1, 2, 6, 24, 135, 930, 7420, 66752, 667485, 7342290, 88107426, 1145396472, 16035550531, 240533257874, 3848532125880, 65425046139840, 1177650830516985, 22375365779822562, 447507315596451070, 9397653627525472280, 206748379805560389951, 4755212735527888968642

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

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

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

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

Maple

a := proc (n) local x, y, t, k; if n <= 1 then 0 else x := 0; 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[Sinh[Log[1/(1-x)]-x], {x, 0, nn}], x] (* Geoffrey Critzer, Jun 23 2014 *)

Crossrefs

Cf. A000166, A216778 (derangements with even number of cycles).

Sequence in context: A277211 A370017 A343482 * A129101 A292907 A216507

Adjacent sequences: A216776 A216777 A216778 * A216780 A216781 A216782

Keyword

nonn,easy

Author

José H. Nieto S., Sep 16 2012

Status

approved