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G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = 1/(1 - a(0)*x^a(0)/(1 - a(1)*x^a(1)/(1 - a(2)*x^a(2)/(1 - ...)))), a continued fraction.
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%I #4 Aug 23 2017 23:42:44

%S 1,1,2,4,10,24,60,148,376,944,2392,6032,15280,38608,97728,247104,

%T 625312,1581568,4001680,10122624,25610368,64787520,163907904,

%U 414654848,1049031104,2653873152,6713958912,16985280000,42970438432,108708830336,275018076928,695755635328,1760162851328

%N G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = 1/(1 - a(0)*x^a(0)/(1 - a(1)*x^a(1)/(1 - a(2)*x^a(2)/(1 - ...)))), a continued fraction.

%e G.f. = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 24*x^5 + 60*x^6 + ... = 1/(1 - x/(1 - x/(1 - 2*x^2/(1 - 4*x^4/(1 - 10*x^10/(1 - ...)))))).

%Y Cf. A213411, A213435.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Aug 23 2017