A298245 Expansion of e.g.f. exp(cos(tanh(x))-1) (even powers only).

1, -1, 12, -327, 15883, -1202524, 130394253, -19113418989, 3632485387276, -867280709024131, 253803272212372575, -89250842789856565620, 37105568909251258810585, -17991614679286735149423193, 10057557723279565571532112044, -6417980557539322347015938082111

Offset: 0

Author

Ilya Gutkovskiy, Jan 15 2018

Keywords

• sign

Examples

			exp(cos(tanh(x))-1) = 1 - x^2/2! + 12*x^4/4! - 327*x^6/6! + 15883*x^8/8! - 1202524*x^10/10! + ...
		

Crossrefs

Cf. A003711, A009090, A009201, A009202, A009203, A009204, A009238, A009239, A009240, A009241, A009254, A297214, A297215.

Programs

Mathematica

nmax = 15; Table[(CoefficientList[Series[Exp[Cos[Tanh[x]] - 1], {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(cos(tanh(x))-1).