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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. 3
1, 1, 8, 129, 3748, 172385, 11541246, 1060864189, 128254619480, 19735654508577, 3766841223919930, 873355411013249021, 241783431463815426516, 78781867440446089479937, 29844928122224237593463270, 13007143530120743289176560125, 6462200434400107274026753685296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) ~ sqrt(Pi) * 2^(n+1) * n^(2*n + 1/2) / exp(2*n - 1/2). - Vaclav Kotesovec, Aug 09 2021

MATHEMATICA

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

CROSSREFS

Cf. A295238, A295241, A295242.

Sequence in context: A338328 A073701 A239756 * A240630 A187609 A241076

Adjacent sequences:  A295237 A295238 A295239 * A295241 A295242 A295243

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 18 2017

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)