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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
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OFFSET
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1,2
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COMMENTS
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Number of standard tableaux of shape (n,n,1,1,1,1) (see Stanley reference). - Emeric Deutsch, May 20 2004
Number of increasing tableaux of shape (n+4,n+4) with largest entry 2n+4. An increasing tableau is a semistandard tableau with strictly increasing rows and columns, such that the set of entries forms an initial segment of the positive integers. - Oliver Pechenik, May 02 2014
a(n) = number of noncrossing partitions of 2n+4 into n 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 and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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D-finite with recurrence (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
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a[n_] := (n+1)(n+2)(n+3)*Binomial[2n+4, n-1]/24; Table[a[n], {n, 1, 19}](* Jean-François Alcover, Nov 16 2011 *)
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PROG
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(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
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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Offset is correct!
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STATUS
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approved
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