OFFSET
0,3
FORMULA
E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arcsinh(x^(k/d))^d / d).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 + ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) ArcSinh[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 17 2019
STATUS
approved