A352691 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + log(1 + x).

1, -3, 5, -23, 204, -1894, 16862, -166466, 2346712, -37858296, 558727872, -9031080288, 185546362416, -3960341036352, 83728926109488, -1961110591316304, 50908186083448320, -1384998141007364736, 38998680958184088960, -1160052698286814237056, 37029733866954589964544

Offset: 1

Author

Ilya Gutkovskiy, May 15 2022

Keywords

• sign

Crossrefs

Cf. A157159, A157164, A348205, A348206, A352404, A352664, A352953.

Programs

Mathematica

nmax = 21; 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.