A322470 - OEIS

%I #16 Jan 29 2020 03:55:20

%S 1,-1,3,-8,4,236,-3892,54552,-739440,9704088,-116868648,1033709040,

%T 4025264736,-592337009328,23033374965456,-708140910086400,

%U 19418661884145024,-485092601562305664,10704418782304457088,-180835985547961196544,431827528992523301376,162896031123325288266240

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

%H Vaclav Kotesovec, <a href="/A322470/b322470.txt">Table of n, a(n) for n = 0..416</a>

%H Vaclav Kotesovec, <a href="/A322470/a322470.jpg">Plot of (abs(a(n))/n!)^(1/n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>

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

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

%Y Cf. A007325, A048594, A301923, A322342.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Dec 19 2018