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A216779 Number of derangements on n elements with an odd number of cycles. 1
0, 0, 1, 2, 6, 24, 135, 930, 7420, 66752, 667485, 7342290, 88107426, 1145396472, 16035550531, 240533257874, 3848532125880, 65425046139840, 1177650830516985, 22375365779822562, 447507315596451070, 9397653627525472280, 206748379805560389951, 4755212735527888968642 (list; graph; refs; listen; history; text; internal format)
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: A191343 A052862 A277211 * A129101 A292907 A216507

Adjacent sequences:  A216776 A216777 A216778 * A216780 A216781 A216782

KEYWORD

nonn,easy

AUTHOR

José H. Nieto S., Sep 16 2012

STATUS

approved

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Last modified September 18 20:22 EDT 2019. Contains 327181 sequences. (Running on oeis4.)