OFFSET
0,1
COMMENTS
For t in open interval (0,1) we have:
y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2).
y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2.
y(t) = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1.
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..54301
Omer Gimenez, Marc Noy, Asymptotic enumeration and limit laws of planar graphs, J. Amer. Math. Soc. 22 (2009), 309-329.
FORMULA
y(A266389) = 1, where function t->y(t) is defined in the Comments section.
EXAMPLE
0.62637166330...
PROG
(PARI)
y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2);
y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2;
y(t) = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1;
N=83; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);
eval(Vec(Str(t0))[3..-101]) \\ Gheorghe Coserea, Sep 03 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Gheorghe Coserea, Dec 28 2015
STATUS
approved