A296842 Expansion of e.g.f. cos(x*tan(x/2)) (even powers only).

1, 0, -3, -15, -14, 1755, 60357, 1740284, 45816165, 776485557, -37342503290, -7203185712261, -822818831400759, -85463040449605000, -8640073895507612019, -843669753827174738535, -73050419139737972150438, -3478007209663880122501701

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (2*n)! * [x^(2*n)] cos(x*tan(x/2)).

Example

cos(x*tan(x/2)) = 1 - 3*x^4/4! - 15*x^6/6! - 14*x^8/8! + 1755*x^10/10! + 60357*x^12/12! + ...

Mathematica

nmax = 17; Table[(CoefficientList[Series[Cos[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

Crossrefs

Cf. A001469, A003710, A009080, A110501, A296839, A296841.

Sequence in context: A099476 A063628 A280201 * A279925 A279534 A181404

Adjacent sequences: A296839 A296840 A296841 * A296843 A296844 A296845

Keyword

sign

Author

Ilya Gutkovskiy, Dec 21 2017

Status

approved