A341914 - OEIS

A341914

Number of partitions of n into 10 distinct and relatively prime parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 97, 128, 164, 212, 267, 340, 423, 530, 653, 807, 984, 1204, 1455, 1761, 2112, 2534, 3015, 3590, 4242, 5013, 5888, 6912, 8070, 9418, 10936, 12690, 14663, 16928, 19466, 22367, 25608, 29292, 33401, 38047, 43214, 49037, 55494, 62740, 70760, 79725, 89623

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OFFSET

55,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 55..1000

FORMULA

G.f.: Sum_{k>=1} mu(k)* x^(55*k) / Product_{j=1..10} (1 - x^(j*k)).

a(n) <= A008639(n-55), equality for n<110. - R. J. Mathar, Feb 28 2021

MATHEMATICA

nmax = 108; CoefficientList[Series[Sum[MoebiusMu[k] x^(55 k)/Product[1 - x^(j k), {j, 1, 10}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 55] &

CROSSREFS