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A023035
Number of compositions of n into 10 ordered relatively prime parts.
10
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
OFFSET
10,2
LINKS
N. J. A. Sloane, Transforms
FORMULA
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
MAPLE
with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 9), d=divisors(n)):
seq(a(n), n=10..50); # Alois P. Heinz, Feb 05 2020
MATHEMATICA
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 *)
PROG
(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 9):d in Divisors(n)]:n in[10..42]]; // Marius A. Burtea, Feb 07 2020
KEYWORD
nonn
STATUS
approved