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A089433
Number of noncrossing connected graphs on n nodes having exactly two interior faces.
2
2, 30, 315, 2856, 23940, 191268, 1480050, 11196900, 83304936, 611931320, 4450217772, 32104210320, 230080173960, 1639890119016, 11634355574100, 82216112723640, 579022013389050, 4065827626164150, 28475852003986695
OFFSET
4,1
LINKS
P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 203-229, 1999.
FORMULA
a(n) = n*binomial(3n-3, n-4)/2.
D-finite with recurrence -2*(2*n+1)*(n-4)*a(n) +3*(3*n-4)*(3*n-5)*a(n-1)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(4)=2 because the only connected graphs on the nodes A,B,C,D having exactly two interior faces are {AB,BC,CD,DA,AC} and {AB,BC,CD,DA,BD}.
PROG
(PARI) a(n) = n*binomial(3*n-3, n-4)/2; \\ Michel Marcus, Oct 26 2015
CROSSREFS
Column k=2 of A089434.
Cf. A007297.
Sequence in context: A189770 A245020 A277660 * A152277 A230610 A231597
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 28 2003
STATUS
approved