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

0,3

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f.: exp(Sum_{k>=1} Sum_{d|k} arctanh(x^(k/d))^d / d).

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]!

Crossrefs

Cf. A010050, A203716, A330537.

Sequence in context: A143463 A290444 A270665 * A141716 A129102 A129099

Adjacent sequences: A330535 A330536 A330537 * A330539 A330540 A330541

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 17 2019

Status

approved