%I #5 Dec 21 2017 14:55:36
%S 1,1,4,33,451,9110,253401,9246881,427272364,24332740569,1671761966755,
%T 136185663849422,12966840876896193,1425738305622057713,
%U 179172604156015950676,25507107918052543195905,4081610970381242583997171,729135575105289450378655526
%N Expansion of e.g.f. exp(x*tan(x/2)) (even powers only).
%F a(n) = (2*n)! * [x^(2*n)] exp(x*tan(x/2)).
%e exp(x*tan(x/2)) = 1 + x^2/2! + 4*x^4/4! + 33*x^6/6! + 451*x^8/8! + ...
%t nmax = 17; Table[(CoefficientList[Series[Exp[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%Y Cf. A001469, A003723, A006229, A009252, A009273, A110501, A296836.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 21 2017