A089433 Number of noncrossing connected graphs on n nodes having exactly two interior faces.

2, 30, 315, 2856, 23940, 191268, 1480050, 11196900, 83304936, 611931320, 4450217772, 32104210320, 230080173960, 1639890119016, 11634355574100, 82216112723640, 579022013389050, 4065827626164150, 28475852003986695

Offset: 4

Author

Emeric Deutsch, Dec 28 2003

Keywords

• nonn

Examples

			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}.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 4..200
• P. Flajolet and M. Noy, Analytic combinatorics of non-crossing configurations, Discrete Math., 204, 203-229, 1999.

Crossrefs

Column k=2 of A089434.

Cf. A007297.

Programs

PARI

a(n) = n*binomial(3*n-3, n-4)/2; \\ Michel Marcus, Oct 26 2015

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