|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|