A033278 Number of diagonal dissections of an n-gon into 6 regions.

0, 132, 1287, 7007, 28028, 91728, 259896, 659736, 1534896, 3325608, 6789783, 13180167, 24496472, 43835792, 75869640, 127481640, 208606320, 333316620, 521215695, 799197399, 1203649524, 1783184480, 2601993680, 3743934480, 5317472160, 7461614160, 10352989647

Offset: 7

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of standard tableaux of shape (n-6,2,2,2,2,2) (n>=8). - Emeric Deutsch, May 20 2004

Number of short bushes with n+4 edges and 6 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(8)=132 because the only short bushes with 12 edges and 6 branch nodes are the one-hundred-thirty-two full binary trees with 12 edges. Column 6 of A108263. - Emeric Deutsch, May 29 2005

Links

• T. D. Noe, Table of n, a(n) for n = 7..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

PARI

vector(40, n, n+=6; binomial(n+4, 5)*binomial(n-3, 5)/6) \\ Michel Marcus, Jun 18 2015

Formula

a(n) = binomial(n+4, 5)*binomial(n-3, 5)/6.

G.f.: z^8(132-165z+110z^2-44z^3+10z^4-z^5)/(1-z)^11. - Emeric Deutsch, May 29 2005