A296464 Expansion of e.g.f. arcsin(arcsin(x)) (odd powers only).

1, 2, 28, 1024, 71632, 8192736, 1392793920, 330041217024, 104069101383936, 42159457593506304, 21346870862961183744, 13213529766600134344704, 9818417126704155249954816, 8625630408510010165396070400, 8844234850947343105068735283200, 10467364426053362392901751845683200

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

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

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

a(n) ~ sqrt(2) * (2*n)! / (sqrt(Pi*sin(2)*n) * sin(1)^(2*n)). - Vaclav Kotesovec, Dec 13 2017

Example

arcsin(arcsin(x)) = x/1! + 2*x^3/3! + 28*x^5/5! + 1024*x^7/7! + 71632*x^9/9! + ...

Mathematica

nmax = 16; Table[(CoefficientList[Series[ArcSin[ArcSin[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
nmax = 16; Table[(CoefficientList[Series[-I Log[Log[I x + Sqrt[1 - x^2]] + Sqrt[1 + Log[I x + Sqrt[1 - x^2]]^2]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Crossrefs

Cf. A001818, A003712, A012063, A296466.

Sequence in context: A362587 A009403 A026944 * A292806 A113633 A186491

Adjacent sequences: A296461 A296462 A296463 * A296465 A296466 A296467

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 13 2017

Status

approved