A354118 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + arctanh(x).

1, -2, 2, -8, 64, -544, 3968, -29952, 378880, -5938176, 68247552, -793491456, 15949529088, -306908848128, 4760383438848, -90615249567744, 2119956936523776, -49428158281678848, 1123874181449515008, -26217392043061149696, 722523072906903158784, -21323712124731229470720, 589068777481530305937408

Offset: 1

Author

Ilya Gutkovskiy, May 17 2022

Keywords

• sign

Crossrefs

Cf. A010050, A353821, A353928, A354066, A354115, A354116, A354117.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + ArcTanh[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 + arctanh(x^k)) / k.