A354056 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + sinh(x).

1, -2, 1, -4, 21, -196, 1023, -5440, 65145, -1237456, 10925883, -69882880, 1994183205, -39099282496, 372390766023, -6270496768000, 158096182329585, -3268815510804736, 64115697136312563, -1009052458754375680, 27389518837925527965, -924645800211698308096, 19391677044464348893503

Offset: 1

Author

Ilya Gutkovskiy, May 16 2022

Keywords

• sign

Crossrefs

Cf. A003704, A353608, A353910, A354055, A354063, A354064, A354065, A354066.

Programs

Mathematica

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