A291840 Decimal expansion of the constant c in the asymptotic formula for A291839.
2, 2, 6, 2, 8, 7, 5, 8, 3, 2, 5, 6, 2, 6, 2, 1, 2, 4, 6, 3, 0, 2, 3, 3, 3, 3, 5, 8, 3, 8, 4, 3, 6, 5, 9, 3, 8, 9, 0, 6, 8, 0, 4, 1, 9, 6, 3, 9, 5, 3, 7, 1, 0, 5, 2, 7, 1, 2, 7, 1, 6, 3, 3, 4, 1, 8, 5, 4, 7, 3, 8, 9, 7, 1, 2, 9, 9, 4, 8
Offset: 1
Examples
2.262875832562621246302333358384...
Links
- Gheorghe Coserea, Table of n, a(n) for n = 1..55000
- E. A. Bender, Z. Gao and N. C. Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43.
Programs
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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; }; alpha(t) = 144 + 592*t + 664*t^2 + 135*t^3 + 6*t^4 - 5*t^5; mu(t) = { my(mu1 = (1+t) * (3+t)^2 * (1+2*t)^2 * (1+3*t)^2 / t^3, y0 = y(t)); mu1 * y0 / ((1 + y0) * alpha(t)); }; N=79; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1); c=mu(t0); eval(select(x->(x != "."), Vec(Str(c))[1..-101]))