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Search: id:A002056
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| A002056 |
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Number of diagonal dissections of a convex n-gon into n-5 regions.
(Formerly M4941 N2115)
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+0
5
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| 1, 14, 120, 825, 5005, 28028, 148512, 755820, 3730650, 17978180, 84987760, 395482815, 1816357725, 8250123000, 37119350400, 165645101160, 733919156190, 3231337461300, 14147884842000, 61636377252450
(list; graph; listen)
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OFFSET
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6,2
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COMMENT
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Number of standard tableaux of shape (n-5,n-5,1,1,1) (see Stanley reference). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 20 2004
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REFERENCES
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D. Beckwith, Legendre polynomials and polygon dissections?, Amer. Math. Monthly, 105 (1998), 256-257.
A. Cayley, On the partitions of a polygon, Proc. London Math. Soc., 22 (1891), 237-262 = Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 93ff.
P. Lisonek, Closed forms for the number of polygon dissections. Journal of Symbolic Computation 20 (1995), 595-601.
R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 370-388.
R. P. Stanley, Polygon dissections and standard Young tableaux, J. Comb. Theory, Ser. A, 76, 175-177, 1996.
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LINKS
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T. D. Noe, Table of n, a(n) for n=6..100
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FORMULA
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a(n)=binomial(n-3, 3)*binomial(2n-7, n-6)/(n-5).
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CROSSREFS
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Sequence in context: A073383 A022642 A004312 this_sequence A125377 A126535 A041001
Adjacent sequences: A002053 A002054 A002055 this_sequence A002057 A002058 A002059
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KEYWORD
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nonn
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AUTHOR
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njas
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