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

1,2

Links

Table of n, a(n) for n=1..23.

Formula

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

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

Crossrefs

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

Sequence in context: A354055 A053565 A116603 * A158356 A015939 A261059

Adjacent sequences: A354053 A354054 A354055 * A354057 A354058 A354059

Keyword

sign

Author

Ilya Gutkovskiy, May 16 2022

Status

approved