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A023033 Number of compositions of n into 8 ordered relatively prime parts. 8
1, 8, 36, 120, 330, 792, 1716, 3432, 6434, 11440, 19440, 31824, 50352, 77520, 116160, 170544, 244826, 346104, 479908, 657792, 886314, 1184040, 1557312, 2035800, 2623140, 3365736, 4260608, 5379616, 6704742, 8347680, 10263648, 12619464 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

LINKS

Marius A. Burtea, Table of n, a(n) for n = 8..5000

N. J. A. Sloane, Transforms

FORMULA

Moebius transform of C(n-1,7).

G.f.: Sum_{k>=1} mu(k) * x^(8*k) / (1 - x^k)^8. - Ilya Gutkovskiy, Feb 05 2020

MAPLE

with(numtheory):

a:= n-> add(mobius(n/d)*binomial(d-1, 7), d=divisors(n)):

seq(a(n), n=8..50);  # Alois P. Heinz, Feb 05 2020

MATHEMATICA

a[n_]:=DivisorSum[n, Binomial[# - 1, 7] MoebiusMu[n/#]&]; Array[a, 37, 8] (* or *) a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k - 1, 7], {k, 1, n}]; Table[a[n], {n, 8, 45}] (* Vincenzo Librandi, Feb 07 2020 *)

PROG

(MAGMA) [&+[MoebiusMu(n div d)*Binomial(d-1, 7):d in Divisors(n)]:n in[8..40]]; // Marius A. Burtea, Feb 07 2020

CROSSREFS

Cf. A000741, A000742, A000743, A023031, A023032, A023034, A023035.

Sequence in context: A008500 A306941 A008490 * A278971 A000580 A290995

Adjacent sequences:  A023030 A023031 A023032 * A023034 A023035 A023036

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)