A296466 Expansion of e.g.f. arcsinh(arcsin(x)) (odd powers only).

1, 0, 8, 56, 8000, 342144, 68623488, 8295676416, 2411783847936, 584142614728704, 240810283258527744, 96772676958798741504, 54867909992513301282816, 32661008325245409302937600, 24691868812821871169667072000, 20243305132513358736699378892800, 19829947398943934886214249532620800

Offset

0,3

Links

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

Formula

E.g.f.: arcsin(arcsinh(x)) (odd powers only, absolute values).

E.g.f.: log(sqrt(1 - log(i*x + sqrt(1 - x^2))^2) - i*log(i*x + sqrt(1 - x^2))), where i is the imaginary unit (odd powers only).

a(n) ~ 2 * (2*n)! / sqrt(Pi*(4 + Pi^2)*n). - Vaclav Kotesovec, Dec 13 2017

Example

arcsinh(arcsin(x)) = x/1! + 8*x^5/5! + 56*x^7/7! + 8000*x^9/9! + 342144*x^11/11! + 68623488*x^13/13! + ...

Mathematica

nmax = 17; Table[(CoefficientList[Series[ArcSinh[ArcSin[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
nmax = 17; Table[(CoefficientList[Series[Log[Sqrt[1 - Log[I x + Sqrt[1 - x^2]]^2] - I Log[I x + Sqrt[1 - x^2]]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Crossrefs

Cf. A001818, A003722, A012248, A296464.

Sequence in context: A154411 A105850 A009089 * A202863 A244958 A043071

Adjacent sequences: A296463 A296464 A296465 * A296467 A296468 A296469

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 13 2017

Status

approved