OFFSET
3,2
REFERENCES
Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 424, see B(x).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 3..200
Bodirsky, M., Giménez, O., Kang, M., & Noy, M., The asymptotic number of outerplanar graphs and series-parallel graphs, in Proceedings of European Conference on Combinatorics, Graph Theory, and Applications (EuroComb05), DMTCS Proceedings Volume AE (pp. 383-388). [Cached copy, with permission]
M. Bodirsky and M. Kang, The asymptotic number of outerplanar graphs. [Only the abstract has been archived]
M. Drmota, O. Gimenez, Marc Noy, Vertices of given degree in series-parallel graphs, Random Struct. Algor. 36 (3) (2010), 251-371, Lemma 2.3
Steven R. Finch, Planar graph growth constants.
FORMULA
Recurrence known, see Bodirsky and Kang.
E.g.f.: (-3+2*x-3*x^2)/16+(3-x)*sqrt(1-6*x+x^2)/16+log((3-x-sqrt(1-6*x+x^2))/2)/2. - Vladeta Jovovic, Jun 26 2007
a(n) ~ 2^(-5/2) * sqrt(3*sqrt(2)-4) * (1+sqrt(2))^(2*n-2) * n^(n-2) / exp(n). - Vaclav Kotesovec, Nov 05 2016
MATHEMATICA
offset = 3; terms = 15; egf = (-3 + 2*x - 3*x^2)/16 + (3 - x)*(Sqrt[1 - 6*x + x^2]/16) + Log[(3 - x - Sqrt[1 - 6*x + x^2])/2]/2; Drop[ CoefficientList[ egf + O[x]^(terms + offset), x]*Range[0, terms + offset - 1]!, offset] (* Jean-François Alcover, Nov 05 2016, after Vladeta Jovovic *)
PROG
(PARI) seq(n)={Vec(serlaplace(intformal((1 + 5*x - sqrt(1 - 6*x + x^2 + O(x^n)))/8 - x)))} \\ Andrew Howroyd, Feb 12 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Steven Finch, Sep 08 2004
EXTENSIONS
Terms a(18) and beyond from Andrew Howroyd, Feb 12 2021
STATUS
approved