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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Formula

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

Example

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 + ...

Crossrefs

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

Sequence in context: A006027 A049124 A275756 * A163134 A370446 A150128

Adjacent sequences: A301624 A301625 A301626 * A301628 A301629 A301630

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 24 2018

Status

approved