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%I #9 Apr 08 2018 09:11:49
%S 1,1,2,6,20,71,265,1024,4059,16414,67451,280856,1182379,5024361,
%T 21522055,92833874,402879747,1757852317,7706728006,33932931008,
%U 149986338830,665276977574,2960306454110,13210976195068,59114318997648,265166069469324,1192145264317628,5370983954821322
%N G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x)/(1 - x^2*A(x)^2/(1 - x^3*A(x)^3/(1 - x^4*A(x)^4/(1 - ...))))), a continued fraction.
%H Vaclav Kotesovec, <a href="/A301627/b301627.txt">Table of n, a(n) for n = 0..500</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rogers-RamanujanContinuedFraction.html">Rogers-Ramanujan Continued Fraction</a>
%F a(n) ~ c * d^n / n^(3/2), where d = 4.760595370947474723688065553003203505424287110594102605580439495640678... and c = 0.395762805862214496152624315213041270339036... - _Vaclav Kotesovec_, Apr 08 2018
%e G.f. A(x) = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 71*x^5 + 265*x^6 + 1024*x^7 + 4059*x^8 + 16414*x^9 + 67451*x^10 + ...
%e log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 55*x^4/4 + 236*x^5/5 + 1035*x^6/6 + 4593*x^7/7 + 20551*x^8/8 + ... + A291653(n)*x^n/n + ...
%Y Cf. A005169, A192728, A192737, A291653, A301362, A301629.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 24 2018
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