A296853 Expansion of e.g.f. tanh(x*tan(x/2)) (even powers only).

0, 1, 1, -27, -403, 8345, 688473, -208019, -3189211931, -162605047455, 28806493001105, 5257860587364341, -288068264497990179, -230932276247139756887, -14420179324444754436023, 13944106915630111553887485, 3643613240568912544562868053

Offset: 0

Author

Ilya Gutkovskiy, Dec 21 2017

Keywords

• sign

Examples

			tanh(x*tan(x/2)) = x^2/2! + x^4/4! - 27*x^6/6! - 403*x^8/8! + 8345*x^10/10! + ...
		

Crossrefs

Cf. A000182, A001469, A003721, A009817, A110501, A296839, A296841, A296842, A296854, A296856.

Programs

Mathematica

nmax = 16; Table[(CoefficientList[Series[Tanh[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)] tanh(x*tan(x/2)).