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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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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, 267325773340626, 1154761882042824, 4969989654817600
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OFFSET
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6,2
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COMMENTS
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Number of standard tableaux of shape (n-5,n-5,1,1,1) (see Stanley reference). - Emeric Deutsch, May 20 2004
Number of increasing tableaux of shape (n-2,n-2) with largest entry 2n-7. An increasing tableau is a semistandard tableau with strictly increasing rows and columns, and set of entries an initial segment of the positive integers. - Oliver Pechenik, May 02 2014
Number of noncrossing partitions of 2n-7 into n-5 blocks all of size at least 2. - Oliver Pechenik, May 02 2014
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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.
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FORMULA
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a(n) = binomial(n-3, 3)*binomial(2n-7, n-6)/(n-5).
G.f.: (x-1+(1-11*x+40*x^2-50*x^3+10*x^4)*(1-4*x)^(-5/2))/(2*x^5). - Mark van Hoeij, Oct 25 2011
D-finite with recurrence: -(n-1)*(n-5)*(n-6)*a(n) +2*(2*n-7)*(n-3)*(n-4)*a(n-1)=0. - R. J. Mathar, Feb 16 2020
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MAPLE
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MATHEMATICA
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Table[Binomial[n - 3, 3] Binomial[2n - 7, n - 6]/(n - 5), {n, 6, 50}] (* Indranil Ghosh, Apr 11 2017 *)
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PROG
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(Magma) [Binomial(n-3, 3)*Binomial(2*n-7, n-6)/(n-5): n in [6..30]]; // Vincenzo Librandi, Feb 18 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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