A296835 Expansion of e.g.f. exp(x*tan(x/2)) (even powers only).

1, 1, 4, 33, 451, 9110, 253401, 9246881, 427272364, 24332740569, 1671761966755, 136185663849422, 12966840876896193, 1425738305622057713, 179172604156015950676, 25507107918052543195905, 4081610970381242583997171, 729135575105289450378655526

Offset: 0

Author

Ilya Gutkovskiy, Dec 21 2017

Keywords

• nonn

Examples

			exp(x*tan(x/2)) = 1 + x^2/2! + 4*x^4/4! + 33*x^6/6! + 451*x^8/8! + ...
		

Crossrefs

Cf. A001469, A003723, A006229, A009252, A009273, A110501, A296836.

Programs

Mathematica

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}]

Formula

a(n) = (2*n)! * [x^(2*n)] exp(x*tan(x/2)).