%I #7 Sep 26 2017 03:14:18
%S 1,1,3,5,11,27,63,143,341,799,1865,4417,10401,24433,57619,135749,
%T 319683,753427,1775207,4182359,9855389,23222687,54718921,128937361,
%U 303821873,715906625,1686933723,3975020013,9366551195,22070960907,52007117407,122547413479,288765804957,680436157615
%N Expansion of 1/(1 - x - 2*x^2/(1 - 3*x^3 - 4*x^4/(1 - 5*x^5 - 6*x^6/(1 - 7*x^7 - 8*x^8/(1 - ...))))), a continued fraction.
%F a(n) ~ c * d^n, where d = 2.35636016857596143712421472862749989350673596686819... and c = 0.353844135039289092297842723019941866883167102736... - _Vaclav Kotesovec_, Sep 25 2017
%t nmax = 33; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-2 k x^(2 k), 1 - (2 k + 1) x^(2 k + 1), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A088352, A088357.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 25 2017