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A023034 Number of compositions of n into 9 ordered relatively prime parts. 8

%I

%S 1,9,45,165,495,1287,3003,6435,12870,24309,43758,75573,125970,203445,

%T 319770,490149,735471,1081080,1562274,2218788,3108105,4289133,5852925,

%U 7882290,10518255,13871286,18156204,23511345,30260340,38564262,48902997

%N Number of compositions of n into 9 ordered relatively prime parts.

%H Marius A. Burtea, <a href="/A023034/b023034.txt">Table of n, a(n) for n = 9..5000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

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

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

%p with(numtheory):

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

%p seq(a(n), n=9..50); # _Alois P. Heinz_, Feb 05 2020

%t 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 *)

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

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

%K nonn

%O 9,2

%A _David W. Wilson_

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Last modified September 20 17:47 EDT 2020. Contains 337265 sequences. (Running on oeis4.)