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Search: id:A007160
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| A007160 |
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Number of diagonal dissections of a convex (n+6)-gon into n regions.
(Formerly M5094)
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+0
5
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| 1, 20, 225, 1925, 14014, 91728, 556920, 3197700, 17587350, 93486536, 483367885, 2442687975, 12109051500, 59053512000, 283963030560, 1348824395160, 6338392712550, 29503515951000, 136173391604250
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of standard tableaux of shape (n,n,1,1,1,1) (see Stanley reference). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 20 2004
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. Beckwith, Legendre polynomials and polygon dissections?, Amer. Math. Monthly, 105 (1998), 256-257.
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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FORMULA
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(n+5)(n-1)*n*a(n)=2(2n+3)(n+3)(n+2)a(n-1).
a(n)=binomial(n+3, 4)*binomial(2n+4, n-1)/n.
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CROSSREFS
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A diagonal of A033282.
Sequence in context: A000833 A054329 A112503 this_sequence A023018 A073386 A022648
Adjacent sequences: A007157 A007158 A007159 this_sequence A007161 A007162 A007163
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Offset is correct!
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