A296836 Expansion of e.g.f. exp(x*tanh(x/2)) (even powers only).

1, 1, 2, 3, -3, 20, 105, -5271, 133826, -2714517, 25525845, 2131781300, -235250824479, 17527695547713, -1124258412169438, 58383380825728035, -975024061456732035, -398903577787777972396, 97649546210035758250281, -17069419358223320552890167

Offset: 0

Author

Ilya Gutkovskiy, Dec 21 2017

Keywords

• sign

Examples

			exp(x*tanh(x/2)) = 1 + x^2/2! + 2*x^4/4! + 3*x^6/6! - 3*x^8/8! + ...
		

Crossrefs

Cf. A001469, A003723, A006229, A009252, A009273, A110501, A296835.

Programs

Mathematica

nmax = 19; Table[(CoefficientList[Series[Exp[x Tanh[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*tanh(x/2)).