OFFSET
7,2
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.
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
PROG
(PARI) vector(40, n, n+=6; binomial(n+4, 5)*binomial(n-3, 5)/6) \\ Michel Marcus, Jun 18 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved