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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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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. P. Stanley, Polygon dissections and standard Young tableaux, J. Comb. Theory, Ser. A, 76, 175-177, 1996.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..150
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FORMULA
| (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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MATHEMATICA
| a[n_] := (n+1)(n+2)(n+3)*Binomial[2n+4, n-1]/24; Table[a[n], {n, 1, 19}](* From Jean-François Alcover, Nov 16 2011 *)
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PROG
| (MAGMA) [Binomial(n+3, 4)*Binomial(2*n+4, n-1)/n : n in [1..30]]; // Vincenzo Librandi, Nov 17 2011
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CROSSREFS
| A diagonal of A033282.
Sequence in context: A178261 A054329 A112503 * A195265 A023018 A073386
Adjacent sequences: A007157 A007158 A007159 * A007161 A007162 A007163
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Offset is correct!
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