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%I #19 Jul 21 2018 23:38:22
%S 1,-1,13,-181,3865,-140521,6324517,-344747677,23853473329,
%T -1996865965009,193406280000061,-21615227339380357,
%U 2778071540350106953,-403985610499148666041,65635628800688339178325
%N Expansion of E.g.f.: cos(x*cos(x)) (even powers only).
%H G. C. Greubel, <a href="/A009015/b009015.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = Sum_{j=0..(2*n-1)/2} binomial(2*n,2*j)*((Sum_{i=0..((2*j-1)/2)} (j-i)^(2*n-2*j)*binomial(2*j,i)))*(-1)^(n))/(2^(4*j-2*n-1)))+(-1)^n. - _Vladimir Kruchinin_, Jun 06 2011
%p seq(coeff(series(factorial(n)*(cos(x*cos(x))), x,n+1),x,n),n=0..30,2); # _Muniru A Asiru_, Jul 21 2018
%t With[{nmax = 60}, CoefficientList[Series[Cos[x*Cos[x]], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]] (* _G. C. Greubel_, Jul 21 2018 *)
%o (Maxima)
%o a(n):=sum(binomial(2*n,2*j)*((sum((j-i)^(2*n-2*j)*binomial(2*j,i),i,0,((2*j-1)/2)))*(-1)^(n))/(2^(4*j-2*n-1)),j,0,(2*n-1)/2)+(-1)^n; /* _Vladimir Kruchinin_, Jun 06 2011 */
%o (PARI) x='x+O('x^50); v=Vec(serlaplace(cos(x*cos(x)))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, Jul 21 2018
%K sign
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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