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%I #6 Sep 16 2021 14:33:48
%S 1,1,2,4,10,24,64,164,440,1164,3128,8368,22552,60624,163528,440768,
%T 1189616,3210000,8667296,23400304,63196192,170668608,460972768,
%U 1245085184,3363190688,9084616128,24540062528,66289885504,179071151872,483733046208,1306740302848,3529993576448,9535868752256
%N Expansion of 1/(1 - x/(1 - x/(1 - 2*x^2/(1 - 2*x^2/(1 - 3*x^3/(1 - 3*x^3/(1 - ...))))))), a continued fraction.
%F a(n) ~ c * d^n, where d = 2.7014053577058965980816004348205865476643047417470551135866... and c = 0.1473934094237780704912896884660893313026695094814554837... - _Vaclav Kotesovec_, Sep 16 2021
%t nmax = 32; CoefficientList[Series[1/(1 + ContinuedFractionK[-Floor[(k + 1)/2] x^Floor[(k + 1)/2], 1, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000142, A006958, A088357.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Oct 30 2017
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