A301627 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.

1, 1, 2, 6, 20, 71, 265, 1024, 4059, 16414, 67451, 280856, 1182379, 5024361, 21522055, 92833874, 402879747, 1757852317, 7706728006, 33932931008, 149986338830, 665276977574, 2960306454110, 13210976195068, 59114318997648, 265166069469324, 1192145264317628, 5370983954821322

Offset: 0

Author

Ilya Gutkovskiy, Mar 24 2018

Keywords

• nonn

Examples

			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 + ...
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 + ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..500
• Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Crossrefs

Cf. A005169, A192728, A192737, A291653, A301362, A301629.

Formula

a(n) ~ c * d^n / n^(3/2), where d = 4.760595370947474723688065553003203505424287110594102605580439495640678... and c = 0.395762805862214496152624315213041270339036... - Vaclav Kotesovec, Apr 08 2018