OFFSET
0,1
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..51001
Omer Gimenez, Marc Noy, Asymptotic enumeration and limit laws of planar graphs, J. Amer. Math. Soc. 22 (2009), 309-329.
FORMULA
Equals lim Var(Xn)/n, where Xn is the number of edges of a random labeled planar graph with n vertices.
Equals Kl(A266389), where function t->Kl(t) is defined in the PARI code.
EXAMPLE
0.4303471697292...
PROG
(PARI)
A266389= 0.6263716633;
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;
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));
Km(t) = -R'(t)/(R(t)*Y'(t));
Kl(t) = (-R''(t) + R'(t)*Y''(t)/Y'(t))/(R(t)*Y'(t)^2) + Km(t) + Km(t)^2;
Kl(A266389)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Gheorghe Coserea, Jan 13 2016
STATUS
approved