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%I #5 Dec 17 2019 19:11:06
%S 1,1,4,17,112,769,7088,66387,763600,9164721,126474672,1820139771,
%T 29458146408,494179557897,9100332756552,174762729699459,
%U 3612983961103776,77711328568772193,1784695351000035744,42494646959739633771
%N Expansion of e.g.f. Product_{k>=1} 1 / (1 - arcsinh(x^k)).
%F E.g.f.: exp(Sum_{k>=1} Sum_{d|k} arcsinh(x^(k/d))^d / d).
%t nmax = 19; CoefficientList[Series[Product[1/(1 - ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t 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]!
%Y Cf. A001818, A330515, A330534.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 17 2019
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