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A332470 a(n) = Sum_{d|n} mu(n/d) * binomial(n+d-2, n-1). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..27.

FORMULA

a(n) = [x^n] Sum_{k>=1} mu(k) * x^k / (1 - x^k)^n.

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.

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 August 3 05:48 EDT 2020. Contains 336197 sequences. (Running on oeis4.)