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%I #7 Aug 09 2021 04:37:08
%S 1,1,8,141,4588,238785,18187146,1907650213,263668859560,
%T 46443551748129,10155810113182990,2699369066774377701,
%U 857103398097311042316,320421972956640538172449,139308015910536411839444194,69693570411751759009119119685,39753354051615620993914808710096
%N 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.
%H Vaclav Kotesovec, <a href="/A295242/b295242.txt">Table of n, a(n) for n = 0..200</a>
%F 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
%t nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[-k x Exp[k x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A295240, A295241.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Nov 18 2017