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 A003709 E.g.f. cos(sin(x)) (even powers only). (Formerly M3986) 4

%I M3986

%S 1,-1,5,-37,457,-8169,188685,-5497741,197920145,-8541537105,

%T 432381471509,-25340238127989,1699894200469849,-129076687233903673,

%U 10989863562589199389,-1041327644107761435101

%N E.g.f. cos(sin(x)) (even powers only).

%C a(n) is the number of ways to partition the set {1,2,...,2n} into an even number of odd size blocks. - _Geoffrey Critzer_, Apr 11 2010

%C Unsigned sequence has e.g.f. cosh(sinh(x)) (even powers only).

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 8th line of table.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A003709/b003709.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = sum(j=0..n, (2^(2*j+1)*sum(i=0..(n-j), (i-n+j)^(2*n)*binomial((2*n-2*j),i)*(-1)^(n-i))/(2*n-2*j)!)), n>0, a(1)=0. - _Vladimir Kruchinin_, Jun 08 2011

%t Take[With[{nn=40},CoefficientList[Series[Cos[Sin[x]],{x,0,nn}],x] Range[0,nn]!],{1,-1,2}] (* _Harvey P. Dale_, Sep 18 2011 *)

%o (Maxima)

%o a(n):=sum((2^(2*j+1)*sum((i-n+j)^(2*n)*binomial((2*n-2*j),i)*(-1)^(n-i),i,0,(n-j))/(2*n-2*j)!),j,0,n); /* _Vladimir Kruchinin, Jun 08 2011 */

%K sign

%O 0,3

%A _R. H. Hardin_, _Simon Plouffe_

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Last modified December 12 00:07 EST 2018. Contains 318052 sequences. (Running on oeis4.)