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A023035
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Number of compositions of n into 10 ordered relatively prime parts.
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10
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1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620, 92377, 167960, 293920, 497420, 817135, 1307504, 2042755, 3124550, 4686110, 6906900, 10013002, 14307150, 20155070, 28048790, 38555660, 52451256, 70583095, 94143280, 124355000
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OFFSET
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10,2
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LINKS
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FORMULA
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Moebius transform of C(n-1,9).
G.f.: Sum_{k>=1} mu(k) * x^(10*k) / (1 - x^k)^10. - Ilya Gutkovskiy, Feb 05 2020
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MAPLE
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with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 9), d=divisors(n)):
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MATHEMATICA
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a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k -1, 9], {k, 1, n}]; Table[a[n], {n, 10, 45}] (* or *) Table[a[n], {n, 9, 45}] a[n_]:=DivisorSum[n, Binomial[#-1, 9] MoebiusMu[n/#]&]; Array[a, 37, 10] (* Vincenzo Librandi, Feb 08 2020 *)
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PROG
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(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 9):d in Divisors(n)]:n in[10..42]]; // Marius A. Burtea, Feb 07 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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