A295242 Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 2*x*exp(2*x)/(1 - 3*x*exp(3*x)/(1 - 4*x*exp(4*x)/(1 - ...))))), a continued fraction.
1, 1, 8, 141, 4588, 238785, 18187146, 1907650213, 263668859560, 46443551748129, 10155810113182990, 2699369066774377701, 857103398097311042316, 320421972956640538172449, 139308015910536411839444194, 69693570411751759009119119685, 39753354051615620993914808710096
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..200
Programs
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Mathematica
nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[-k x Exp[k x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
Formula
a(n) ~ c * d^n * n^(2*n + 1/2) / exp(2*n), where d = 2.299007884747807311341155634117203393915283915595348... and c = 3.800670014949659244559370644121796775146171755... - Vaclav Kotesovec, Aug 09 2021