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Search: id:A002055
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| A002055 |
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Number of diagonal dissections of a convex n-gon into n-4 regions.
(Formerly M4639 N1982)
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+0
5
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| 1, 9, 56, 300, 1485, 7007, 32032, 143208, 629850, 2735810, 11767536, 50220040, 212952285, 898198875, 3771484800, 15775723920, 65770848990, 273420862110, 1133802618000, 4691140763400, 19371432850770, 79850555673174
(list; graph; listen)
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OFFSET
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5,2
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COMMENT
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Number of standard tableaux of shape (n-4,n-4,1,1) (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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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=5..100
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FORMULA
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a(n)=binomial(n-3, 2)*binomial(2*n-6, n-5)/(n-4).
With offset 0, this has a(n)=(n+2)*C(2n+4,n)/2 and e.g.f. dif(dif(x*dif(exp(2x)*Bessel_I(2,2x),x),x),x)/2. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2007
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CROSSREFS
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a(n)=f(n, n+1) where f is given in A034261.
Sequence in context: A041148 A114026 A097556 this_sequence A026842 A026846 A026849
Adjacent sequences: A002052 A002053 A002054 this_sequence A002056 A002057 A002058
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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