A023035 Number of compositions of n into 10 ordered relatively prime parts.

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

Marius A. Burtea, Table of n, a(n) for n = 10..5000

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

Crossrefs

Cf. A000741, A000742, A000743, A023031, A023032, A023033, A023034.

Cf. A023023, A023024, A023025, A023026, A023027, A023028, A023029, A023030.

Sequence in context: A289380 A008502 A008492 * A128936 A000582 A229890

Adjacent sequences: A023032 A023033 A023034 * A023036 A023037 A023038

Keyword

nonn

Author

David W. Wilson

Status

approved