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URL: https://oeis.org/A266389

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A266389
Solution of the equation y(t) = 1, where function y(t) is defined in the Comments section.
12
6, 2, 6, 3, 7, 1, 6, 6, 3, 3, 0, 6, 4, 5, 1, 6, 6, 5, 8, 9, 2, 9, 9, 7, 8, 5, 0, 4, 5, 0, 3, 9, 5, 6, 1, 1, 6, 7, 2, 0, 8, 3, 1, 7, 8, 9, 3, 9, 8, 6, 0, 1, 4, 1, 1, 6, 1, 7, 8, 9, 8, 5, 4, 4, 9, 1, 7, 5, 2, 1, 5, 3, 0, 0, 2, 4, 2, 7, 7, 6, 7, 9, 0
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
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