A354116 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + arcsinh(x).

1, -2, -1, 4, -11, 116, -547, 960, -7751, 414384, -3258663, -6813696, -390445563, 9694641984, -964154427, 208258646016, -18431412645519, 207842731632384, -6436900596281679, -37454668211552256, 834261829219880829, 91517388643567641600, -1149793471388581053219

Offset: 1

Author

Ilya Gutkovskiy, May 17 2022

Keywords

• sign

Crossrefs

Cf. A001818, A296435, A353819, A353914, A354056, A354115, A354117, A354118.

Programs

Mathematica

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