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%I #13 Jul 26 2022 12:55:54
%S 2,30,315,2856,23940,191268,1480050,11196900,83304936,611931320,
%T 4450217772,32104210320,230080173960,1639890119016,11634355574100,
%U 82216112723640,579022013389050,4065827626164150,28475852003986695
%N Number of noncrossing connected graphs on n nodes having exactly two interior faces.
%H Andrew Howroyd, <a href="/A089433/b089433.txt">Table of n, a(n) for n = 4..200</a>
%H P. Flajolet and M. Noy, <a href="http://dx.doi.org/10.1016/S0012-365X(98)00372-0">Analytic combinatorics of non-crossing configurations</a>, Discrete Math., 204, 203-229, 1999.
%F a(n) = n*binomial(3n-3, n-4)/2.
%F 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
%e 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}.
%o (PARI) a(n) = n*binomial(3*n-3, n-4)/2; \\ _Michel Marcus_, Oct 26 2015
%Y Column k=2 of A089434.
%Y Cf. A007297.
%K nonn
%O 4,1
%A _Emeric Deutsch_, Dec 28 2003
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