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Search: id:A137207
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| A137207 |
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Number of exceptional sets of roots of type D_n. Also the number of unordered factorizations of the Coxeter element. |
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+0
1
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| 12, 87, 584, 3835, 25008, 162792, 1060048, 6910695, 45119100, 295038315, 1932260256, 12673336052, 83236707232, 547388545740, 3604063891104, 23755630474079, 156740823815940, 1035157282013085, 6842413166034600
(list; graph; listen)
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OFFSET
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3,1
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LINKS
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F. Chapoton Cluster algebras
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FORMULA
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a(n) = (2*(n-1)/(2*n-1))*binomial(3*n-3,n-1)-binomial(3*n-5,n-2)+4*binomial(3*n-3,n-3)
a(n) = (16*n^2-41*n+24)/(n*(2*n-1))*binomial(3*n-5,n-2)
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EXAMPLE
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a(3)=12 because D3 is the same as A3.
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PROGRAM
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modu_NC_D:=proc(n) begin (16*n*n-41*n+24)/n/(2*n-1)*binomial(3*n-5, n-2) end;
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CROSSREFS
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Cf. A001764, A045721.
Adjacent sequences: A137204 A137205 A137206 this_sequence A137208 A137209 A137210
Sequence in context: A104911 A091119 A046023 this_sequence A082814 A057406 A125349
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KEYWORD
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nonn
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AUTHOR
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F. Chapoton (fchapoton(AT)voila.fr), Mar 05 2008
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