A330544 Expansion of e.g.f. Product_{k>=1} (1 + arctanh(x^k)).
1, 1, 2, 14, 48, 424, 3360, 30288, 276864, 3591936, 46241280, 599212800, 9205954560, 142744412160, 2554915184640, 47649718609920, 907617573273600, 18296536869273600, 413470794456760320, 9130651338347642880, 221996730181563187200
Offset: 0
Keywords
Programs
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Mathematica
nmax = 20; CoefficientList[Series[Product[(1 + ArcTanh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! 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]!
Formula
E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arctanh(x^(k/d))^d / d).