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A023035 Number of compositions of n into 10 ordered relatively prime parts. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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