A354115 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + arcsin(x).

1, -2, 1, -4, 29, -244, 1583, -10368, 124553, -2029776, 20127867, -180343296, 3978820221, -75977108544, 914656587063, -15574206480384, 370244721585681, -8082505243732224, 162968423791332339, -3082360882836013056, 82014901819948738629, -2501342802748968883200, 58311771938510122952559

Offset: 1

Author

Ilya Gutkovskiy, May 17 2022

Keywords

• sign

Crossrefs

Cf. A001818, A353818, A353913, A354055, A354116, A354117, A354118.

Programs

Mathematica

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