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A268619
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a(n) = (1/n^2) * Sum_{d|n} moebius(n/d)*binomial(2*d,d).
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6
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2, 1, 2, 4, 10, 25, 70, 200, 600, 1845, 5830, 18772, 61542, 204659, 689410, 2347920, 8074762, 28009524, 97909318, 344615860, 1220539390, 4347310451, 15564141262, 55985418344, 202256970300, 733607281875, 2670698800548, 9755982857964, 35751803209918, 131405090455065, 484316704740126, 1789672012052256
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OFFSET
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1,1
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COMMENTS
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6*a(n) is divisible by n (cf. A268592).
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := DivisorSum[n, MoebiusMu[n/#] * Binomial[2*#, #] &] / n^2; Array[a, 35] (* Amiram Eldar, Aug 24 2023 *)
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PROG
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(PARI) { a(n) = sumdiv(n, d, moebius(n/d)*binomial(2*d, d))/n^2; }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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