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 A106520 a(n) = A068875(n-1) - A003239(n). 0
 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; refs; listen; history; text; internal format)
 OFFSET 5,1 COMMENTS 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. LINKS F. Chapoton, On some anticyclic operads, Algebraic and Geometric Topology 5 (2005), paper no. 4, pages 53-69. FORMULA a(n) = 1/n * binomial(2*n-2, n-1) * 2 - 1/(2*n) * sum(d divides n, phi(d) * binomial(2*n/d, n/d) ). EXAMPLE a(6)=4. MAPLE 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: MATHEMATICA a[n_] :=  If[n <= 1, 0, 1/n*Binomial[2*n-2, n-1]*2 - 1/(2*n)*DivisorSum[n, EulerPhi[#]*Binomial[2*n/#, n/#]&]]; Table[a[n], {n, 5, 30}] (* Jean-François Alcover, Feb 20 2017 *) CROSSREFS Cf. A000108, A001761. Sequence in context: A240316 A151449 A045664 * A301802 A318249 A093045 Adjacent sequences:  A106517 A106518 A106519 * A106521 A106522 A106523 KEYWORD nonn AUTHOR F. Chapoton, May 30 2005 STATUS approved

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Last modified May 30 18:07 EDT 2020. Contains 334728 sequences. (Running on oeis4.)