A291836 Decimal expansion of exponential growth rate of the number of 2-connected planar graphs on n labeled nodes.

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

Offset: 2

Author

Gheorghe Coserea, Sep 03 2017

Keywords

• nonn
• cons

Examples

			26.18411255565814849687701423391145...
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 2..55001
• E. A. Bender, Z. Gao and N. C. Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43.

Crossrefs

Cf. A096331, A266389, A291835.

Programs

PARI

x(t)     = (1+3*t)*(1/t-1)^3/16;
y(t)     = {
  my(y1  = t^2 * (1-t) * (18 + 36*t + 5*t^2),
     y2  = 2 * (3+t) * (1+2*t) * (1+3*t)^2);
  (1+2*t)/((1+3*t) * (1-t)) * exp(-y1/y2) - 1;
};
N=80; default(realprecision, N+100); t0=solve(t=.62, .63, y(t)-1);
r=1/x(t0); eval(select(x->(x != "."), Vec(Str(r))[1..-101]))

Formula

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

Constant r where A096331(n) ~ A291835 * n^(-7/2) * r^n * n!.