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Search: id:A033277
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| A033277 |
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Number of diagonal dissections of an n-gon into 5 regions. |
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+0
4
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| 0, 42, 330, 1485, 5005, 14014, 34398, 76440, 157080, 302940, 554268, 969969, 1633905, 2662660, 4214980, 6503112, 9806280, 14486550, 21007350, 29954925, 42063021, 58241106, 79606450, 107520400
(list; graph; listen)
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OFFSET
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6,2
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COMMENT
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Number of standard tableaux of shape (n-5,2,2,2,2) (n>=7). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 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 (deutsch(AT)duke.poly.edu), May 29 2005
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REFERENCES
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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.
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FORMULA
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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 (deutsch(AT)duke.poly.edu), May 29 2005
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CROSSREFS
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Cf. A108263.
Sequence in context: A064369 A036463 A095266 this_sequence A134386 A105919 A091082
Adjacent sequences: A033274 A033275 A033276 this_sequence A033278 A033279 A033280
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KEYWORD
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nonn
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AUTHOR
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njas
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