|
%I #15 Jun 23 2014 15:38:52
%S 0,0,1,2,6,24,135,930,7420,66752,667485,7342290,88107426,1145396472,
%T 16035550531,240533257874,3848532125880,65425046139840,
%U 1177650830516985,22375365779822562,447507315596451070,9397653627525472280,206748379805560389951,4755212735527888968642
%N Number of derangements on n elements with an odd number of cycles.
%F a(n+1) = n*(a(n) + a(n-1) - n + 2), a(0)=0, a(1)=0.
%F a(n) = (A000166(n) + n - 1)/2.
%F E.g.f.: sinh(log(1/(1-x)) - x). - _Geoffrey Critzer_, Jun 23 2014
%p 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;
%t nn=23;Range[0,nn]!CoefficientList[Series[Sinh[Log[1/(1-x)]-x],{x,0,nn}],x] (* _Geoffrey Critzer_, Jun 23 2014 *)
%Y Cf. A000166, A216778 (derangements with even number of cycles).
%K nonn,easy
%O 0,4
%A _José H. Nieto S._, Sep 16 2012
|
