A296841 Expansion of e.g.f. sin(x*tan(x/2)) (even powers only).

0, 1, 1, -12, -193, -2365, -18552, 500689, 48649969, 2981261772, 169237306055, 9187565146331, 427287357700176, 6011297159973313, -2887128048794477663, -711942625068679870620, -132369975517302093882097, -22968753773651295426439021

Offset: 0

Author

Ilya Gutkovskiy, Dec 21 2017

Keywords

• sign

Examples

			sin(x*tan(x/2)) = x^2/2! + x^4/4! - 12*x^6/6! - 193*x^8/8! - 2365*x^10/10! - 18552*x^12/12! + ...
		

Crossrefs

Cf. A001469, A003706, A009515, A110501, A296839, A296842.

Programs

Mathematica

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