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A033277 Number of diagonal dissections of an n-gon into 5 regions. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

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

Table of n, a(n) for n=6..35.

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.

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

PROG

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

CROSSREFS

Cf. A108263.

Sequence in context: A095266 A232338 A252937 * A190533 A190602 A134386

Adjacent sequences:  A033274 A033275 A033276 * A033278 A033279 A033280

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 20 09:59 EDT 2019. Contains 322309 sequences. (Running on oeis4.)