A266758 E.g.f.: x*(1+x-(x^2-6*x+1)^(1/2))/8 + x^2/2.

0, 0, 2, 3, 36, 660, 16200, 496440, 18204480, 776381760, 37726819200, 2056693161600, 124267145587200, 8240599586419200, 594942538116326400, 46448183595445632000, 3898894095328167936000, 350138974362304038912000, 33495869457535946452992000, 3400528750619249753247744000

Offset

0,3

Comments

This is the exponential generating function for rooted biconnected outerplanar graphs.

References

Bernasconi, Nicla, Konstantinos Panagiotou, and Angelika Steger. "On the degree sequences of random outerplanar and series-parallel graphs." In Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques, LNCS 5171, pp. 303-316. Springer Berlin Heidelberg, 2008.

Links

Table of n, a(n) for n=0..19.

V. Kurauskas, On graphs containing few disjoint excluded minors. Asymptotic number and structure of graphs containing few disjoint minors K_4, arXiv preprint arXiv:1504.08107 [math.CO], 2015. See Section 8.1.

Formula

a(n) = -(1/8)*GegenbauerC(n-1,-1/2,3)*n!, for n>2. - Benedict W. J. Irwin, Jul 20 2016

a(n) ~ 2^(-9/4) * (1 + sqrt(2))^(2*n - 3) * n^(n-1) / exp(n). - Vaclav Kotesovec, Jun 05 2019

D-finite with recurrence a(n) +6*(-n+3)*a(n-1) +(n^2-58*n+189)*a(n-2) +9*(n-2)*(n-5)*a(n-3)=0. - R. J. Mathar, Aug 20 2021

Mathematica

Join[{0, 0, 2}, Table[-(1/8) GegenbauerC[-1 + n, -(1/2), 3] n!, {n, 3, 30}]] (* Benedict W. J. Irwin, Jul 20 2016 *)

Crossrefs

Sequence in context: A118443 A355236 A340845 * A280539 A216145 A109748

Adjacent sequences: A266755 A266756 A266757 * A266759 A266760 A266761

Keyword

nonn

Author

N. J. A. Sloane, Jan 03 2016

Status

approved