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%I #5 Dec 17 2019 19:11:20
%S 1,1,4,20,136,1024,10208,103872,1287424,17001984,252383232,3971122176,
%T 69973813248,1281307791360,25646098022400,540521184067584,
%U 12170993370955776,286967313311858688,7206454521728335872,188326525698968518656
%N Expansion of e.g.f. Product_{k>=1} 1 / (1 - arctanh(x^k)).
%F E.g.f.: exp(Sum_{k>=1} Sum_{d|k} arctanh(x^(k/d))^d / d).
%t nmax = 19; CoefficientList[Series[Product[1/(1 - ArcTanh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 19; CoefficientList[Series[Exp[Sum[Sum[ArcTanh[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A010050, A203716, A330537.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 17 2019