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.
1, 1, 8, 129, 3748, 172385, 11541246, 1060864189, 128254619480, 19735654508577, 3766841223919930, 873355411013249021, 241783431463815426516, 78781867440446089479937, 29844928122224237593463270, 13007143530120743289176560125, 6462200434400107274026753685296
Offset: 0
Keywords
Programs
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Mathematica
nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[-k x Exp[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
Formula
a(n) ~ sqrt(Pi) * 2^(n+1) * n^(2*n + 1/2) / exp(2*n - 1/2). - Vaclav Kotesovec, Aug 09 2021