A266390 Decimal expansion of exponential growth rate of number of labeled planar graphs on n vertices.

2, 7, 2, 2, 6, 8, 7, 7, 7, 6, 8, 5, 8, 8, 5, 7, 6, 4, 6, 7, 0, 7, 9, 4, 5, 8, 0, 5, 1, 4, 9, 4, 4, 5, 8, 2, 8, 7, 4, 8, 9, 8, 0, 1, 5, 8, 7, 7, 8, 6, 8, 3, 6, 0, 1, 0, 7, 2, 4, 0, 8, 6, 9, 4, 3, 6, 1, 9, 3, 3, 4, 9, 7, 6, 2, 6, 2, 3, 1, 3, 7, 2, 1

Offset: 2

Author

Gheorghe Coserea, Dec 28 2015

Keywords

• nonn
• cons

Examples

			27.2268777685...
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 2..51000
• Omer Giménez, Marc Noy, Estimating the Growth Constant of Labelled Planar Graphs, Mathematics and Computer Science III, Part of the series Trends in Mathematics 2004, pp. 133-139.
• Omer Gimenez, Marc Noy, Asymptotic enumeration and limit laws of planar graphs, J. Amer. Math. Soc. 22 (2009), 309-329.

Crossrefs

Cf. A066537, A266389, A266391.

Programs

PARI

A266389= 0.6263716633;
A1(t)  = log(1+t) * (3*t-1) * (1+t)^3 / (16*t^3);
A2(t)  = log(1+2*t) * (1+3*t) * (1-t)^3 / (32*t^3);
A3(t)  = (1-t) * (185*t^4 + 698*t^3 - 217*t^2 - 160*t + 6);
A4(t)  = 64*t * (1+3*t)^2 * (3+t);
A(t)   = A1(t) + A2(t) + A3(t) / A4(t);
R(t)   = 1/16 * sqrt(1+3*t) * (1/t - 1)^3 * exp(A(t));
1/R(A266389)

Formula

Equals 1/R(A266389), where function t->R(t) is defined in the PARI code.

A066537(n) ~ A266391 * A266390^n * n^(-7/2) * n!.