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A033278
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Number of diagonal dissections of an n-gon into 6 regions.
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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, 2601993680, 3743934480, 5317472160, 7461614160, 10352989647
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OFFSET
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7,2
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COMMENTS
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Number of standard tableaux of shape (n-6,2,2,2,2,2) (n>=8). - Emeric Deutsch, 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, May 29 2005
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LINKS
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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, May 29 2005
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PROG
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(PARI) vector(40, n, n+=6; binomial(n+4, 5)*binomial(n-3, 5)/6) \\ Michel Marcus, Jun 18 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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