A332470 a(n) = Sum_{d|n} mu(n/d) * binomial(n+d-2, n-1).

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

Offset: 1

Author

Ilya Gutkovskiy, Feb 13 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A007438, A008683, A117108, A117109, A332508, A343547.

Programs

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

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}]

PARI

a(n) = sumdiv(n, d, moebius(n/d)*binomial(n+d-2, n-1)); \\ Michel Marcus, Feb 14 2020

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