OFFSET
0,2
FORMULA
E.g.f.: arcsinh(x)*arctan(x) (even powers only, absolute values).
E.g.f.: i*(log(1 - x) - log(1 + x))*log(i*x + sqrt(1 - x^2))/2, where i is the imaginary unit (even powers only).
a(n) ~ Pi * (2*n-1)! / 2. - Vaclav Kotesovec, Dec 13 2017
EXAMPLE
arcsin(x)*arctanh(x) = 2*x^2/2! + 12*x^4/4! + 238*x^6/6! + 9912*x^8/8! + 708282*x^10/10! + ...
MATHEMATICA
nmax = 16; Table[(CoefficientList[Series[ArcSin[x] ArcTanh[x], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
nmax = 16; Table[(CoefficientList[Series[I (Log[1 - x] - Log[1 + x]) Log[I x + Sqrt[1 - x^2]]/2, {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 13 2017
STATUS
approved