A295240 - OEIS

A295240

Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 2*x*exp(x)/(1 - 3*x*exp(x)/(1 - 4*x*exp(x)/(1 - ...))))), a continued fraction.

%I #7 Aug 09 2021 04:19:18

%S 1,1,8,129,3748,172385,11541246,1060864189,128254619480,

%T 19735654508577,3766841223919930,873355411013249021,

%U 241783431463815426516,78781867440446089479937,29844928122224237593463270,13007143530120743289176560125,6462200434400107274026753685296

%N Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 2*x*exp(x)/(1 - 3*x*exp(x)/(1 - 4*x*exp(x)/(1 - ...))))), a continued fraction.

%F a(n) ~ sqrt(Pi) * 2^(n+1) * n^(2*n + 1/2) / exp(2*n - 1/2). - _Vaclav Kotesovec_, Aug 09 2021

%t nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[-k x Exp[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A295238, A295241, A295242.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Nov 18 2017