A296854 Expansion of e.g.f. sinh(x*tan(x/2)) (even powers only).

0, 1, 1, 18, 227, 4565, 126648, 4620805, 213569269, 12165013026, 835868220455, 68093897815361, 6483538063860336, 712877916658802713, 89586864207214060057, 12753583150716684461970, 2040805972702652020364603, 364567588100855831300341565

Offset: 0

Author

Ilya Gutkovskiy, Dec 21 2017

Keywords

• nonn

Examples

			sinh(x*tan(x/2)) = x^2/2! + x^4/4! + 18*x^6/6! + 227*x^8/8! + 4565*x^10/10! + ...
		

Crossrefs

Cf. A001469, A003717, A009611, A110501, A296839, A296841, A296842, A296853, A296856.

Programs

Mathematica

nmax = 17; Table[(CoefficientList[Series[Sinh[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)] sinh(x*tan(x/2)).