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%I #23 Mar 18 2024 06:41:58
%S 1,3,23,297,5377,125211,3564311,119923089,4655903809,204870639987,
%T 10075617486167,547693463064633,32607543239954113,2110160087505699339,
%U 147482363058886213079,11071382656533287144481,888443133459417946162561,75894715974405095400952803
%N Expansion of 1/(1 - x - 2*x/(1 - 3*x - 4*x/(1 - 5*x - 6*x/(1 - 7*x - 8*x/(1 - ...))))), a continued fraction.
%F a(n) ~ c * d^n * n^n, where d = 2 / (exp(1) * (2*log(2) - 1)) = 1.9046586137314438905888971496696905186344... and c = 1/sqrt(2*log(2) - 1) = 1.608943581845581629220091... - _Vaclav Kotesovec_, Jul 01 2019, updated Mar 18 2024
%t nmax = 17; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-2 k x, 1 - (2 k + 1) x, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A001147, A001813, A292855.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jun 25 2019
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