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%I #4 Dec 18 2019 09:02:37
%S 1,1,2,14,48,424,3360,30288,276864,3591936,46241280,599212800,
%T 9205954560,142744412160,2554915184640,47649718609920,907617573273600,
%U 18296536869273600,413470794456760320,9130651338347642880,221996730181563187200
%N Expansion of e.g.f. Product_{k>=1} (1 + arctanh(x^k)).
%F E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arctanh(x^(k/d))^d / d).
%t nmax = 20; CoefficientList[Series[Product[(1 + ArcTanh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) ArcTanh[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A010050, A270664, A330543.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Dec 17 2019