OFFSET
0,2
FORMULA
a(n) = (2*n)! * [x^(2*n)] exp(x*arctanh(x)).
a(n) ~ 2^(2*n + 2) * n^(2*n) / exp(2*n). - Vaclav Kotesovec, Dec 21 2017
EXAMPLE
exp(x*arctanh(x)) = 1 + 2*x^2/2! + 20*x^4/4! + 504*x^6/6! + 24464*x^8/8! + ...
MATHEMATICA
nmax = 15; Table[(CoefficientList[Series[Exp[x ArcTanh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
nmax = 15; Table[(CoefficientList[Series[Exp[x (Log[1 + x] - Log[1 - x])/2], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 20 2017
STATUS
approved