A033279 Number of diagonal dissections of an n-gon into 7 regions.

0, 429, 5005, 32032, 148512, 556920, 1790712, 5116320, 13302432, 32008977, 72177105, 153977824, 313112800, 610569960, 1147334760, 2086063200, 3682355040, 6329047725, 10617908301, 17424259776, 28021470400, 44233892560, 68638798800, 104830165440, 157759842240

Offset: 8

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of standard tableaux of shape (n-7,2,2,2,2,2,2) (n>=9). - Emeric Deutsch, May 21 2004

Number of short bushes with n+5 edges and 7 branch nodes (i.e. nodes with outdegree at least 2; a short bush is an ordered tree with no nodes of outdegree 1). Example: a(9)=429 because the only short bushes with 14 edges and 7 branch nodes are the four-hundred-twenty-nine full binary trees with 14 edges. Column 7 of A108263. - Emeric Deutsch, May 29 2005

Links

• T. D. Noe, Table of n, a(n) for n = 8..1000
• D. Beckwith, Legendre polynomials and polygon dissections?, Amer. Math. Monthly, 105 (1998), 256-257.
• F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999), 73-112.

Crossrefs

Cf. A108263.

Programs

Mathematica

Table[(Binomial[n+5,6]Binomial[n-3,6])/7,{n,8,40}] (* Harvey P. Dale, May 27 2013 *)

PARI

vector(40, n, n+=7; binomial(n+5, 6)*binomial(n-3, 6)/7) \\ Michel Marcus, Jun 18 2015

Formula

a(n) = binomial(n+5, 6)*binomial(n-3, 6)/7.

G.f.: z^9(429-572z+429z^2-208z^3+65z^4-12z^5+z^6)/(1-z)^13. - Emeric Deutsch, May 29 2005