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 A332470 a(n) = Sum_{d|n} mu(n/d) * binomial(n+d-2, n-1). 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..1000 FORMULA 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 MATHEMATICA 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}] PROG (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 CROSSREFS Cf. A000010, A007438, A008683, A117108, A117109, A332508, A343547. Sequence in context: A254203 A220903 A042087 * A151465 A151474 A138550 Adjacent sequences:  A332467 A332468 A332469 * A332471 A332472 A332473 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 13 2020 STATUS approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)