A296940 Expansion of e.g.f. sech(x*tan(x/2)) (even powers only).

1, 0, -3, -15, 406, 14355, -189123, -42283696, -837846615, 284972761557, 28521503291230, -3070544172379761, -1054107683427761463, 1143265731049052000, 54900209444888714822181, 7959249060310612253252265, -3679623847504649619798598778, -1631286181830482909037469295781

Offset: 0

Author

Ilya Gutkovskiy, Dec 22 2017

Keywords

• sign

Examples

			sech(x*tan(x/2)) = 1 - 3*x^4/4! - 15*x^6/6! + 406*x^8/8! + ...
		

Crossrefs

Cf. A000364, A001469, A009011, A110501, A296839, A296841, A296842, A296853, A296854, A296856, A296939.

Programs

Mathematica

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