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A179300
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a(n) is the number of corner-rooted hexangulations of girth 6 with n inner faces.
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2
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1, 3, 17, 128, 1131, 11070, 116317, 1287480, 14829188, 176250143, 2148687567, 26750057584, 338939419026, 4359422270652, 56799490825125, 748414965684808, 9959308633462092, 133694287642377756, 1808762770097970724, 24642635223262953600, 337856475305856870275
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OFFSET
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1,2
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LINKS
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FORMULA
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Bouttier-Guittier give an explicit formula.
a(1) = 1, and a(n) = (6*(2*(-2 + n))!/((-2 + n)!*n!))*2F1(-5*n, 2 - n, 2*(2 - n); -1) for n >= 2, where 2F1(a, b, c; z) is the hypergeometric function. - Franck Maminirina Ramaharo, Jan 27 2019
a(n) ~ sqrt(152 - 62*sqrt(6)) * (248*sqrt(6)/9 - 52)^n / (3*sqrt(Pi) * n^(5/2)). - Vaclav Kotesovec, Jun 09 2019
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EXAMPLE
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G.f.: x + 3*x^2 + 17*x^3 + 128*x^4 + 1131*x^5 + 11070*x^6 + ...
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MATHEMATICA
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Join[{1}, Table[(6*(2*(-2 + n))!/((-2 + n)!*n!))*Hypergeometric2F1[-5*n, 2 - n, 2*(2 - n), -1], {n, 2, 50}]] (* Franck Maminirina Ramaharo, Jan 27 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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