A296941 Expansion of e.g.f. arcsin(x*tan(x/2)) (even powers only).

0, 1, 1, 18, 227, 12125, 542448, 55071205, 5492843269, 905996551626, 159770279801855, 39299019878991521, 10721872262093222016, 3707660329253983397113, 1438816154956071399594457, 668949924061617421125859650, 348908555505788456739965412203

Offset

0,4

Links

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

Formula

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

Example

arcsin(x*tan(x/2)) = x^2/2! + x^4/4! + 18*x^6/6! + 227*x^8/8! + ...

Mathematica

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

Crossrefs

Cf. A001469, A001818, A012780, A110501, A296839, A296841, A296842, A296853, A296854, A296856, A296939, A296940, A296942.

Sequence in context: A056950 A021144 A296854 * A016312 A017916 A016307

Adjacent sequences: A296938 A296939 A296940 * A296942 A296943 A296944

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 22 2017

Status

approved