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%I #41 Feb 12 2021 20:00:12
%S 1,9,132,2700,70920,2275560,86264640,3772681920,186972105600,
%T 10355595465600,633892275878400,42495895579737600,3096545573029708800,
%U 243680880958010496000,20596410256606119936000,1860881636529774802944000,178975197401013144907776000,18256461815785805072068608000
%N Number of 2-connected outerplanar graphs on n labeled nodes.
%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 424, see B(x).
%H Andrew Howroyd, <a href="/A097999/b097999.txt">Table of n, a(n) for n = 3..200</a>
%H Bodirsky, M., Giménez, O., Kang, M., & Noy, M., <a href="/A097999/a097999_1.pdf">The asymptotic number of outerplanar graphs and series-parallel graphs</a>, in Proceedings of European Conference on Combinatorics, Graph Theory, and Applications (EuroComb05), DMTCS Proceedings Volume AE (pp. 383-388). [Cached copy, with permission]
%H M. Bodirsky and M. Kang, <a href="http://web.archive.org/web/20050413032311/http://www.informatik.hu-berlin.de/~bodirsky/publications/asymptoticBK.html">The asymptotic number of outerplanar graphs</a>. [Only the abstract has been archived]
%H M. Drmota, O. Gimenez, Marc Noy, <a href="http://dx.doi.org/10.1002/rsa.20290">Vertices of given degree in series-parallel graphs</a>, Random Struct. Algor. 36 (3) (2010), 251-371, Lemma 2.3
%H Steven R. Finch, <a href="/A097999/a097999.pdf">Planar graph growth constants</a>.
%F Recurrence known, see Bodirsky and Kang.
%F 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
%F 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
%t 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_ *)
%o (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
%Y Cf. A097998, A098000.
%K nonn
%O 3,2
%A _Steven Finch_, Sep 08 2004
%E Terms a(18) and beyond from _Andrew Howroyd_, Feb 12 2021
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