A009591 - OEIS

%I #22 Jan 31 2018 03:18:21

%S 0,2,-4,-42,888,-8086,-115468,8863806,-275344656,2488177106,

%T 369676840940,-34139482063962,1691837365047912,-16526563632072646,

%U -7669129653528552220,1088114395890103645710,-87525176659638470236704

%N Expansion of e.g.f. sinh(sin(x)) * sin(x) (even powers only).

%H G. C. Greubel, <a href="/A009591/b009591.txt">Table of n, a(n) for n = 0..250</a>

%F a(n) = 2*Sum_{j=1..n} 4^(n-j)/(2*j-1)!*Sum_{i=0..j-1} (i-j)^(2*n)* binomial(2*j,i)*(-1)^(n+j-i). - _Vladimir Kruchinin_, Jun 09 2011

%t With[{nn=40},Take[CoefficientList[Series[Sinh[Sin[x]]Sin[x],{x,0,nn}],x]Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Dec 08 2012 *)

%o (Maxima)

%o a(n):=2*sum(4^(n-j)/(2*j-1)!*sum((i-j)^(2*n)*binomial(2*j,i)*(-1)^(n+j-i),i,0,j-1),j,1,n); /* _Vladimir Kruchinin_, Jun 09 2011 */

%o (PARI) x='x+O('x^40); v=Vec(serlaplace(sinh(sin(x))*sin(x))); concat([0], vector(#v\2 ,n,v[2*n-1])) \\ _G. C. Greubel_, Jan 30 2018

%K sign

%O 0,2

%A _R. H. Hardin_

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