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A106519
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a(n)=(2/n)*binomial(2n-2,n-1)-(1/2n)*Sum_{d=divisors(n)} mobius(d)*binomial(2*n/d,n/d).
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0
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1, 1, 2, 3, 9, 19, 58, 160, 499, 1527, 4940, 16001, 53187, 178305, 606330, 2079863, 7203864, 25138879, 88367780, 312577245, 1112119079, 3977502767, 14294207172, 51596165898, 186998138529, 680272336906, 2483341820512, 9094756956909
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| A simple formula with no known combinatorial interpretation. This should give the multiplicity of the trivial module in some sequence of modules of dimension (2n-2)!/n! over the symmetric groups S_n induced from modules of dimension (2n-2)!/n!(n-1)! over the cyclic groups C_n.
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EXAMPLE
| a(6)=9
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MAPLE
| a:=proc(n) if n<=1 then 0 else 1/n*binomial(2*n-2, n-1)*2-1/(2*n)*add(mobius(d)*binomial(2*n/d, n/d), d=divisors(n)) end: end:
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MATHEMATICA
| f[n_] := Block[{d = Divisors[n]}, 2Binomial[2n - 2, n - 1]/n - Plus @@ (MoebiusMu[d]*Binomial[2*n/d, n/d])/(2n)]; Table[ f[n], {n, 29}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 31 2005)
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CROSSREFS
| Cf. A001761, A000108.
Sequence in context: A094679 A094812 A079992 * A006866 A121908 A097075
Adjacent sequences: A106516 A106517 A106518 * A106520 A106521 A106522
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KEYWORD
| nonn
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AUTHOR
| Frederic Chapoton (fchapoton(AT)voila.fr), May 30 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 31 2005
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