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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 03 2016
STATUS
approved