A322470 Expansion of e.g.f. 1/(1 + log(1 + x)/(1 + log(1 + x)^2/(1 + log(1 + x)^3/(1 + ...)))), a continued fraction.

1, -1, 3, -8, 4, 236, -3892, 54552, -739440, 9704088, -116868648, 1033709040, 4025264736, -592337009328, 23033374965456, -708140910086400, 19418661884145024, -485092601562305664, 10704418782304457088, -180835985547961196544, 431827528992523301376, 162896031123325288266240

Offset: 0

Author

Ilya Gutkovskiy, Dec 19 2018

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..416
• Vaclav Kotesovec, Plot of (abs(a(n))/n!)^(1/n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Crossrefs

Cf. A007325, A048594, A301923, A322342.

Programs

Mathematica

nmax = 21; CoefficientList[Series[1/(1 + ContinuedFractionK[Log[1 + x]^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A007325(k)*k!.