A301832 G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x)/(1 - x^3*A(x)^3/(1 - x^5*A(x)^5/(1 - x^7*A(x)^7/(1 - ...))))), a continued fraction.

1, 1, 2, 5, 15, 49, 168, 595, 2160, 7998, 30095, 114751, 442402, 1721636, 6753869, 26680262, 106042264, 423750562, 1701476738, 6861334966, 27776206851, 112839216109, 459867381701, 1879624039171, 7703187691979, 31647457638073, 130314986803631, 537730217342715, 2223228743506792

Offset

0,3

Links

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

Charles H. Conley and Valentin Ovsienko, Quiddities of polygon dissections and the Conway-Coxeter frieze equation, arXiv:2107.01234 [math.CO], 2021.

Formula

a(n) = [x^n] (Sum_{k>=0} A143951(k)*x^k)^(n+1)/(n + 1).

a(n) ~ c * d^n / n^(3/2), where d = 4.36034166192381738574769007441081546251391... and c = 0.42401561796424536417811444539653002307... - Vaclav Kotesovec, Nov 04 2021

Example

G.f. A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 49*x^5 + 168*x^6 + 595*x^7 + 2160*x^8 + 7998*x^9 + 30095*x^10 + ...

Crossrefs

Cf. A143951, A301627.

Sequence in context: A369631 A063021 A364833 * A272460 A149937 A149938

Adjacent sequences: A301829 A301830 A301831 * A301833 A301834 A301835

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 27 2018

Status

approved