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%I #21 Jul 24 2018 09:41:13
%S 1,0,-12,120,784,-95040,3292608,-9423232,-9230042880,890079012864,
%T -40083887897600,-2468650419873792,837675174905843712,
%U -109581967679961088000,5834566862721760149504
%N Expansion of e.g.f. cos(x*sin(x)) (even power only).
%H G. C. Greubel, <a href="/A009050/b009050.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = 2*Sum_{k=1..n-1} binomial(2*n,2*k)*(4^(n-2*k)*(-1)^(k)* Sum_{i=0..k-1} (i-k)^(2*n-2*k)*binomial(2*k,i)*(-1)^(n-i)), n>0, a(0)=1. - _Vladimir Kruchinin_, Jun 30 2011
%p seq(coeff(series(factorial(n)*cos(x*sin(x)), x,n+1),x,n),n=0..40,2); # _Muniru A Asiru_, Jul 24 2018
%t With[{nmax = 60}, CoefficientList[Series[Cos[x*Sin[x]], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]] (* _G. C. Greubel_, Jul 23 2018 *)
%o (Maxima)
%o a(n):=if n=0 then 1 else 2*sum(binomial(2*n,2*k)*(4^(n-2*k)*(-1)^(k)*sum((i-k)^(2*n-2*k)*binomial(2*k,i)*(-1)^(n-i),i,0,k-1)),k,1,n-1); /* _Vladimir Kruchinin_, Jun 30 2011 */
%o (PARI) x='x+O('x^60); v=Vec(serlaplace(cos(x*sin(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Jul 23 2018
%o (GAP) Concatenation([1],List([1..15],n->2*Sum([1..n-1],k->Binomial(2*n,2*k)*(4^(n-2*k)*(-1)^k)*Sum([0..k-1],i->(i-k)^(2*n-2*k)*Binomial(2*k,i)*(-1)^(n-i))))); # _Muniru A Asiru_, Jul 24 2018
%K sign
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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