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A216778 Number of derangements on n elements with an even number of cycles. 1
1, 0, 0, 0, 3, 20, 130, 924, 7413, 66744, 667476, 7342280, 88107415, 1145396460, 16035550518, 240533257860, 3848532125865, 65425046139824, 1177650830516968, 22375365779822544, 447507315596451051, 9397653627525472260, 206748379805560389930, 4755212735527888968620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

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 * A056306 A056298 A114479

Adjacent sequences:  A216775 A216776 A216777 * A216779 A216780 A216781

KEYWORD

nonn,easy

AUTHOR

José H. Nieto S., Sep 16 2012

STATUS

approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)