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A332470
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a(n) = Sum_{d|n} mu(n/d) * binomial(n+d-2, n-1).
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7
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1, 1, 5, 16, 69, 226, 923, 3312, 12825, 47896, 184755, 700712, 2704155, 10373455, 40113421, 154946976, 601080389, 2332498482, 9075135299, 35338355380, 137846298360, 538213522254, 2104098963719, 8233142596640, 32247603662625, 126408753954731, 495918514791900
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = [x^n] Sum_{k>=1} mu(k) * x^k / (1 - x^k)^n.
a(n) = |{(x_1, x_2, ... , x_{n-1}) : 1 <= x_1 <= x_2 <= ... <= x_n = n, gcd(x_1, x_2, ... , x_n) = 1}|. - Seiichi Manyama, Apr 20 2021
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MATHEMATICA
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Table[DivisorSum[n, MoebiusMu[n/#] Binomial[n + # - 2, n - 1] &], {n, 1, 27}]
Table[SeriesCoefficient[Sum[MoebiusMu[k] x^k/(1 - x^k)^n, {k, 1, n}], {x, 0, n}], {n, 1, 27}]
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PROG
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(Magma) [&+[MoebiusMu(n div d) *Binomial(n+d-2, n-1):d in Divisors(n)]:n in [1..30]]; // Marius A. Burtea, Feb 13 2020
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(n+d-2, n-1)); \\ Michel Marcus, Feb 14 2020
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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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