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A033276
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Number of diagonal dissections of an n-gon into 4 regions.
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4
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0, 14, 84, 300, 825, 1925, 4004, 7644, 13650, 23100, 37400, 58344, 88179, 129675, 186200, 261800, 361284, 490314, 655500, 864500, 1126125, 1450449, 1848924, 2334500, 2921750, 3627000, 4468464
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,2
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COMMENTS
| Number of standard tableaux of shape (n-4,2,2,2) (n>=6). - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 20 2004
Number of short bushes with n+2 edges and 4 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(6)=14 because the only short bushes with 8 edges and 4 branch nodes are the fourteen full binary trees with 8 edges. Column 4 of A108263. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 29 2005
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REFERENCES
| 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
| a(n)=binomial(n+2, 3)*binomial(n-3, 3)/4
G.f.: z^6(14-14z+6z^2-z^3)/(1-z)^7. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 29 2005
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CROSSREFS
| Cf. A033275, A108263.
Sequence in context: A085036 A107935 A008451 * A006858 A027818 A054149
Adjacent sequences: A033273 A033274 A033275 * A033277 A033278 A033279
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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