A266390 - OEIS

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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

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OFFSET

2,1

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.

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!.

EXAMPLE

27.2268777685...

PROG

(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);