A033281 Number of diagonal dissections of a convex (n+9)-gon into n+1 regions.

1, 35, 616, 7644, 76440, 659736, 5116320, 36581688, 245402157, 1563837275, 9553624080, 56338955400, 322432175520, 1798432526880, 9809631964800, 52470868368240, 275857874141850, 1428186531145374

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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, arXiv:1209.1355 [math.CO].
• 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).