A330535 Expansion of e.g.f. Product_{k>=1} 1 / (1 - arcsinh(x^k)).

1, 1, 4, 17, 112, 769, 7088, 66387, 763600, 9164721, 126474672, 1820139771, 29458146408, 494179557897, 9100332756552, 174762729699459, 3612983961103776, 77711328568772193, 1784695351000035744, 42494646959739633771

Offset: 0

Author

Ilya Gutkovskiy, Dec 17 2019

Keywords

• nonn

Crossrefs

Cf. A001818, A330515, A330534.

Programs

Mathematica

nmax = 19; CoefficientList[Series[Product[1/(1 - ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[Exp[Sum[Sum[ArcSinh[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: exp(Sum_{k>=1} Sum_{d|k} arcsinh(x^(k/d))^d / d).