A352953 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 - log(1 - x).

1, -1, -1, 1, -16, 86, -526, 302, -10424, 323304, -2805408, -6563424, -374664720, 5877455520, 32949033168, -24011091024, -16610113920768, 87369247685760, -5110200130727808, -23241729685643136, 1042965176555775744, 49535245994720788224

Offset: 1

Author

Ilya Gutkovskiy, May 15 2022

Keywords

• sign

Crossrefs

Cf. A157159, A157164, A348205, A348206, A352404, A352664, A352691.

Programs

Mathematica

nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 - Log[1 - x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

Formula

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

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