A330538 Expansion of e.g.f. Product_{k>=1} 1 / (1 - arctanh(x^k)).
1, 1, 4, 20, 136, 1024, 10208, 103872, 1287424, 17001984, 252383232, 3971122176, 69973813248, 1281307791360, 25646098022400, 540521184067584, 12170993370955776, 286967313311858688, 7206454521728335872, 188326525698968518656
Offset: 0
Keywords
Programs
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Mathematica
nmax = 19; CoefficientList[Series[Product[1/(1 - ArcTanh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! 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]!
Formula
E.g.f.: exp(Sum_{k>=1} Sum_{d|k} arctanh(x^(k/d))^d / d).