OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 13 2017
STATUS
approved