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A033280
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Number of diagonal dissections of a convex (n+8)-gon into n+1 regions.
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4
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1, 27, 385, 4004, 34398, 259896, 1790712, 11511720, 70114902, 409003595, 2303105805, 12593413560, 67173369900, 350777861280, 1798432526880, 9073909567440, 45140379405030, 221768094898350, 1077403874372826, 5182007298602904, 24699073588138180, 116759256962107760
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OFFSET
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0,2
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COMMENTS
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Number of standard tableaux of shape (n+1,n+1,1,1,1,1,1) (see Stanley reference). - Emeric Deutsch, May 20 2004
Number of increasing tableaux of shape (n+6,n+6) 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+1 blocks all of size at least 2. - Oliver Pechenik, May 02 2014
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LINKS
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FORMULA
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a(n) = binomial(n+5, 5)*binomial(2n+7, n)/(n+1).
D-finite with recurrence n*(n+7)*(n+1)*a(n) -2*(n+5)*(n+3)*(2*n+7)*a(n-1)=0. - R. J. Mathar, Feb 09 2020
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MATHEMATICA
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Table[(Binomial[n+5, 5]Binomial[2n+7, n])/(n+1), {n, 0, 30}] (* Harvey P. Dale, Oct 16 2016 *)
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PROG
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(PARI) vector(30, n, n--; binomial(n+5, 5)*binomial(2*n+7, n)/(n+1)) \\ Michel Marcus, Jun 18 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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