A354066 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + tanh(x).

1, -2, -2, 8, -24, 224, -720, -1408, 0, 717824, -3628800, -47546368, -479001600, 12431673344, 87178291200, -68669145088, -20922789888000, 47215125069824, -6402373705728000, -159504062197792768, 2432902008176640000, 102176932845365755904, -1124000727777607680000

Offset: 1

Author

Ilya Gutkovskiy, May 16 2022

Keywords

• sign

Crossrefs

Cf. A000182, A353779, A353912, A354055, A354056, A354063, A354064, A354065.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + Tanh[x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

Formula

E.g.f.: Sum_{k>=1} mu(k) * log(1 + tanh(x^k)) / k.