A033277 Number of diagonal dissections of an n-gon into 5 regions.

0, 42, 330, 1485, 5005, 14014, 34398, 76440, 157080, 302940, 554268, 969969, 1633905, 2662660, 4214980, 6503112, 9806280, 14486550, 21007350, 29954925, 42063021, 58241106, 79606450, 107520400, 143629200, 189909720, 248720472, 322858305, 415621185, 530877480

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Number of standard tableaux of shape (n-5,2,2,2,2) (n>=7). - Emeric Deutsch, May 20 2004

Number of short bushes with n+3 edges and 5 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(7)=42 because the only short bushes with 10 edges and 5 branch nodes are the fortytwo full binary trees with 10 edges. Column 5 of A108263. - Emeric Deutsch, May 29 2005

Links

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

Formula

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

G.f.: z^7(42-48z+27z^2-8z^3+z^4)/(1-z)^9. - Emeric Deutsch, May 29 2005