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Search: id:A033278
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| A033278 |
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Number of diagonal dissections of an n-gon into 6 regions. |
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+0
4
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| 0, 132, 1287, 7007, 28028, 91728, 259896, 659736, 1534896, 3325608, 6789783, 13180167, 24496472, 43835792, 75869640, 127481640, 208606320, 333316620, 521215695, 799197399, 1203649524, 1783184480
(list; graph; listen)
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OFFSET
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7,2
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COMMENT
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Number of standard tableaux of shape (n-6,2,2,2,2,2) (n>=8). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 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 (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+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 (deutsch(AT)duke.poly.edu), May 29 2005
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CROSSREFS
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Cf. A108263.
Sequence in context: A158543 A156958 A090199 this_sequence A119982 A129975 A064303
Adjacent sequences: A033275 A033276 A033277 this_sequence A033279 A033280 A033281
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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