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%I #19 Jan 27 2018 06:29:40
%S 0,2,16,392,21376,1875872,227105536,35750690432,7110343684096,
%T 1750588208886272,523940264885702656,187423773435078920192,
%U 78905518064423548911616,38568578386644134655598592
%N Expansion of e.g.f. sinh(tan(x)*tan(x)) (even powers only).
%F a(n) = sum(m=0..n, 1/(2*m+1)!*sum(j=4*m+2..2*n, binomial(j-1,4*m+1)*j!*2^(2*n-j)*(-1)^(n+1+j)*stirling2(2*n,j))). - _Vladimir Kruchinin_, Jun 11 2011
%e sinh(tan(x)*tan(x)) = 2/2!*x^2 + 16/4!*x^4 + 392/6!*x^6 + 21376/8!*x^8 + ...
%t With[{nn=30},Take[CoefficientList[Series[Sinh[Tan[x]^2],{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Jun 12 2016 *)
%o (Maxima)
%o a(n):=sum(1/(2*m+1)!*sum(binomial(j-1,4*m+1)*j!*2^(2*n-j)*(-1)^(n+1+j)*stirling2(2*n,j),j,4*m+2,2*n),m,0,n); /* _Vladimir Kruchinin_, Jun 11 2011 */
%K nonn
%O 0,2
%A _R. H. Hardin_
%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997
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