A296942 Expansion of e.g.f. arcsinh(x*tan(x/2)) (even powers only).

0, 1, 1, -12, -193, 5195, 397248, -9589391, -3147743231, -10931156748, 65632780196255, 4713930109297211, -2846093176389647904, -606335605925899344287, 213167747093485780707937, 109460864600185764327567060, -21782399212761670190907400897

Offset

0,4

Links

Table of n, a(n) for n=0..16.

Formula

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

Example

arcsinh(x*tan(x/2)) = x^2/2! + x^4/4! - 12*x^6/6! - 193*x^8/8! + ...

Mathematica

nmax = 16; Table[(CoefficientList[Series[ArcSinh[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

Crossrefs

Cf. A000364, A001469, A001818, A110501, A296839, A296841, A296842, A296853, A296854, A296856, A296939, A296940, A296941.

Sequence in context: A264603 A296841 A342111 * A159498 A034671 A066230

Adjacent sequences: A296939 A296940 A296941 * A296943 A296944 A296945

Keyword

sign

Author

Ilya Gutkovskiy, Dec 22 2017

Status

approved