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A033281
Number of diagonal dissections of a convex (n+9)-gon into n+1 regions.
4
1, 35, 616, 7644, 76440, 659736, 5116320, 36581688, 245402157, 1563837275, 9553624080, 56338955400, 322432175520, 1798432526880, 9809631964800, 52470868368240, 275857874141850, 1428186531145374
OFFSET
0,2
COMMENTS
Number of standard tableaux of shape (n+1,n+1,1,1,1,1,1,1) (see Stanley reference). - Emeric Deutsch, May 20 2004
Number of increasing tableaux of shape (n+7,n+7) with largest entry 2n+8. 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
a(n) = number of noncrossing partitions of 2n+8 into n+1 blocks all of size at least 2. - Oliver Pechenik, May 02 2014
LINKS
D. Beckwith, Legendre polynomials and polygon dissections?, Amer. Math. Monthly, 105 (1998), 256-257.
O. Pechenik, Cyclic sieving of increasing tableaux and small Schröder paths, J. Combin. Theory A, 125 (2014), 357-378.
R. P. Stanley, Polygon dissections and standard Young tableaux, J. Comb. Theory, Ser. A, 76, 175-177, 1996.
FORMULA
a(n)=binomial(n+6, 6)*binomial(2n+8, n)/(n+1).
CROSSREFS
Sequence in context: A114342 A208617 A010951 * A161648 A162149 A162384
KEYWORD
nonn
AUTHOR
STATUS
approved