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A266758
E.g.f.: x*(1+x-(x^2-6*x+1)^(1/2))/8 + x^2/2.
0
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.
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 03 2016
STATUS
approved