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Search: id:A106520
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| A106520 |
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Simple formula with no known combinatorial interpretation. |
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+0
1
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| 2, 4, 18, 48, 156, 472, 1526, 4852, 16000, 52940, 178276, 605520, 2079862, 7201084, 25138878, 88358520, 312576996, 1112087012, 3977502766, 14294093652, 51596165872, 186997738504, 680272334202, 2483340387644, 9094756956908
(list; graph; listen)
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OFFSET
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5,1
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COMMENT
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This is the multiplicity of the trivial module in a sequence of modules of dimension (2n-2)!/n! over the symmetric groups S_n, induced from modules of dimension (2n-2)!/n!/(n-1)! (Catalan) over the cyclic groups C_n.
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REFERENCES
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F. Chapoton, On some anticyclic operads, Algebraic and Geometric Topology 5 (2005), paper no. 4, pages 53-69.
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FORMULA
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1/n*binomial(2*n-2, n-1)*2-1/(2*n)*add(phi(d)*binomial(2*n/d, n/d), d=divisors(n))
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EXAMPLE
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a(6)=4
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MAPLE
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a:=proc(n) if n<=1 then 0 else 1/n*binomial(2*n-2, n-1)*2-1/(2*n)*add(phi(d)*binomial(2*n/d, n/d), d=divisors(n)) end: end:
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CROSSREFS
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Cf. A000108, A001761.
Adjacent sequences: A106517 A106518 A106519 this_sequence A106521 A106522 A106523
Sequence in context: A143533 A064723 A045664 this_sequence A093045 A083694 A009679
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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), May 30 2005
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