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Search: id:A033279
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| A033279 |
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Number of diagonal dissections of an n-gon into 7 regions. |
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+0
4
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| 0, 429, 5005, 32032, 148512, 556920, 1790712, 5116320, 13302432, 32008977, 72177105, 153977824, 313112800, 610569960, 1147334760, 2086063200, 3682355040, 6329047725, 10617908301, 17424259776
(list; graph; listen)
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OFFSET
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8,2
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COMMENT
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Number of standard tableaux of shape (n-7,2,2,2,2,2,2) (n>=9). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 21 2004
Number of short bushes with n+5 edges and 7 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(9)=429 because the only short bushes with 14 edges and 7 branch nodes are the four-hundred-twenty-nine full binary trees with 14 edges. Column 7 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+5, 6)*binomial(n-3, 6)/7
G.f.: z^9(429-572z+429z^2-208z^3+65z^4-12z^5+z^6)/(1-z)^13. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 29 2005
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CROSSREFS
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Cf. A108263.
Sequence in context: A064061 A115133 A090200 this_sequence A064304 A046018 A142802
Adjacent sequences: A033276 A033277 A033278 this_sequence A033280 A033281 A033282
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KEYWORD
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nonn
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AUTHOR
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njas
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