A009057 - OEIS

%I #22 Jul 24 2018 03:11:56

%S 1,-3,-15,21,1953,32461,77649,-18557595,-894805183,-21405607651,

%T 421226202033,90171090228021,6418365899545825,230309031988304109,

%U -11126456208720437487,-3093396343171182148731,-342554566975833968005503

%N Expansion of e.g.f. x*cos(sinh(x)) (odd powers only).

%H G. C. Greubel, <a href="/A009057/b009057.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = (2*n+1)*Sum_{m=1..2*n} (Sum_{i=0..m} (-1)^(i+m/2)*(m-2*i)^(2*n) *binomial(m, i))/(2^m*m!), n>0, a(0)=1. - _Vladimir Kruchinin_, Jun 29 2011

%t With[{nn=40},Take[CoefficientList[Series[x Cos[Sinh[x]],{x,0,nn}],x] Range[ 0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, May 22 2017 *)

%o (Maxima)

%o a(n):=if n=0 then 1 else (sum((sum((-1)^(i+m/2)*(m-2*i)^(2*n)*binomial(m,i),i,0,m))/(2^m*m!),m,1,2*n))*(2*n+1); /* _Vladimir Kruchinin_, Jun 28 2011 */

%o (PARI) x='x+O('x^60); v=Vec(serlaplace(x*cos(sinh(x)))); vector((#v-1)\2 ,n,v[2*n-1]) \\ _G. C. Greubel_, Jul 23 2018

%K sign

%O 0,2

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997