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A089433
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Number of noncrossing connected graphs on n nodes having exactly two interior faces.
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2
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2, 30, 315, 2856, 23940, 191268, 1480050, 11196900, 83304936, 611931320, 4450217772, 32104210320, 230080173960, 1639890119016, 11634355574100, 82216112723640, 579022013389050, 4065827626164150, 28475852003986695
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OFFSET
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4,1
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LINKS
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FORMULA
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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
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EXAMPLE
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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}.
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PROG
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(PARI) a(n) = n*binomial(3*n-3, n-4)/2; \\ Michel Marcus, Oct 26 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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