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A023034 Number of compositions of n into 9 ordered relatively prime parts. 8
1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24309, 43758, 75573, 125970, 203445, 319770, 490149, 735471, 1081080, 1562274, 2218788, 3108105, 4289133, 5852925, 7882290, 10518255, 13871286, 18156204, 23511345, 30260340, 38564262, 48902997 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

LINKS

Marius A. Burtea, Table of n, a(n) for n = 9..5000

N. J. A. Sloane, Transforms

FORMULA

Moebius transform of C(n-1,8).

G.f.: Sum_{k>=1} mu(k) * x^(9*k) / (1 - x^k)^9. - Ilya Gutkovskiy, Feb 05 2020

MAPLE

with(numtheory):

a:= n-> add(mobius(n/d)*binomial(d-1, 8), d=divisors(n)):

seq(a(n), n=9..50);  # Alois P. Heinz, Feb 05 2020

MATHEMATICA

Table[a[n], {n, 9, 45}]a[n_]:=DivisorSum[n, Binomial[#-1, 8] MoebiusMu[n/#]&]; Array[a, 37, 9] (* or *) a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k-1, 8], {k, 1, n}]; Table[a[n], {n, 9, 45}] (* Vincenzo Librandi, Feb 08 2020 *)

PROG

(MAGMA) [&+[MoebiusMu(n div d)*Binomial(d-1, 8):d in Divisors(n)]:n in[9..39]]; // Marius A. Burtea, Feb 07 2020

CROSSREFS

Cf. A000741, A000742, A000743, A023031, A023032, A023033, A023035.

Sequence in context: A306942 A289354 A008491 * A000581 A306939 A229889

Adjacent sequences:  A023031 A023032 A023033 * A023035 A023036 A023037

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified August 15 09:42 EDT 2020. Contains 336487 sequences. (Running on oeis4.)