A354055 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + sin(x).

1, -2, -1, 4, -19, 164, -659, 1408, -18775, 642224, -3578279, -21642752, -476298835, 11904106304, 25626362581, 68669145088, -20903398375855, 212840905389824, -6399968826052559, -78465506362130432, 1010700510694925525, 101465632831736751104, -1123931378903214542099

Offset: 1

Author

Ilya Gutkovskiy, May 16 2022

Keywords

• sign

Crossrefs

Cf. A170914, A170915, A328186, A328191, A353607, A353873, A354056, A354063, A354064, A354065, A354066.

Programs

Mathematica

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