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 A106519 a(n) = (2/n)*binomial(2n-2,n-1) - (1/2n)*Sum_{d=divisors(n)} mobius(d)*binomial(2*n/d,n/d). 0
 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; text; internal format)
 OFFSET 2,3 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. LINKS EXAMPLE a(6)=9 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: 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}] (* Robert G. Wilson v, May 31 2005 *) PROG (Sage) def a(n):     return binomial(2*n-2, n-1)*2//n - sum(moebius(n//d)*binomial(2*d, d) for d in divisors(n))//(2*n) # F. Chapoton, May 31 2020 CROSSREFS Cf. A001761, A000108. Sequence in context: A307898 A079992 A324374 * A006866 A121908 A231368 Adjacent sequences:  A106516 A106517 A106518 * A106520 A106521 A106522 KEYWORD nonn,changed AUTHOR F. Chapoton, May 30 2005 EXTENSIONS More terms from Robert G. Wilson v, May 31 2005 STATUS approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)