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A033276
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Number of diagonal dissections of an n-gon into 4 regions.
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6
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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, 5466384, 6643175, 8023575, 9634800, 11506704, 13671944
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OFFSET
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5,2
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COMMENTS
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Number of standard tableaux of shape (n-4,2,2,2) (n>=6). - Emeric Deutsch, 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, May 29 2005
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LINKS
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FORMULA
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a(n) = binomial(n+2, 3)*binomial(n-3, 3)/4.
Sum_{n>=6} 1/a(n) = 109/1225.
Sum_{n>=6} (-1)^n/a(n) = 192*log(2)/35 - 4582/1225. (End)
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MATHEMATICA
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Table[(Binomial[n+2, 3]Binomial[n-3, 3])/4, {n, 5, 40}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 14, 84, 300, 825, 1925, 4004}, 40] (* Harvey P. Dale, Mar 13 2014 *)
CoefficientList[Series[x (14 - 14 x + 6 x^2 - x^3)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 15 2014 *)
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PROG
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(Magma) [(Binomial(n+2, 3)*Binomial(n-3, 3))/4: n in [5..50]]; // Vincenzo Librandi, Mar 15 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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