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

0,3

Links

Table of n, a(n) for n=0..20.

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

Cf. A010050, A270664, A330543.

Sequence in context: A188571 A083102 A270666 * A056080 A241232 A163796

Adjacent sequences: A330541 A330542 A330543 * A330545 A330546 A330547

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 17 2019

Status

approved