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%I #17 Jul 24 2018 21:23:55
%S 1,0,-12,-480,-22512,-1224960,-61017792,1438993920,1844639547648,
%T 677206700482560,225542012911531008,76252348319434383360,
%U 26581103125260630233088,9309180001030233433374720
%N Expansion of e.g.f. cos(tan(x)^2) (even powers only).
%H G. C. Greubel, <a href="/A009083/b009083.txt">Table of n, a(n) for n = 0..236</a>
%F a(n) = 2*Sum_{m=0..n} ((-1)^(m)*Sum_{j=4*m..2*n} binomial(j-1,4*m-1)*j!*2^(2*n-j-1)*(-1)^(n+j)*stirling2(2*n,j))/(2*m)!, n>0, a(0)=1. - _Vladimir Kruchinin_, Jun 11 2011
%t With[{nmax = 60}, CoefficientList[Series[Cos[Tan[x]^2], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]] (* _G. C. Greubel_, Jul 24 2018 *)
%o (Maxima)
%o a(n):=2*sum(((-1)^(m)*sum(binomial(j-1,4*m-1)*j!*2^(2*n-j-1)*(-1)^(n+j)*stirling2(2*n,j),j,4*m,2*n))/(2*m)!,m,0,n); /* _Vladimir Kruchinin_, Jun 11 2011 */
%o (PARI) x='x+O('x^60); v=Vec(serlaplace(cos(tan(x)^2))); vector(#v\2,n,v[2*n-1]) \\ _G. C. Greubel_, 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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