Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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