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A330544
Expansion of e.g.f. Product_{k>=1} (1 + arctanh(x^k)).
1
1, 1, 2, 14, 48, 424, 3360, 30288, 276864, 3591936, 46241280, 599212800, 9205954560, 142744412160, 2554915184640, 47649718609920, 907617573273600, 18296536869273600, 413470794456760320, 9130651338347642880, 221996730181563187200
OFFSET
0,3
FORMULA
E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (-1)^(d + 1) * arctanh(x^(k/d))^d / d).
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]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 17 2019
STATUS
approved