%I #5 Nov 18 2017 09:09:59
%S 1,1,6,63,1024,23025,671196,24295537,1059233008,54376011009,
%T 3229888525300,218930722589601,16744189595081928,1431509929349664385,
%U 135727622625718838092,14175933450070804285665,1621447178602905553394656,202067106261905557292228097,27312528199766157940311518436
%N Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - x*exp(2*x)/(1 - x*exp(3*x)/(1 - x*exp(4*x)/(1 - ...))))), a continued fraction.
%t nmax = 18; CoefficientList[Series[1/(1 + ContinuedFractionK[-x Exp[k x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A295240, A295242.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Nov 18 2017