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

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

Cf. A023022, A023030, A023035, A078374, A101271, A339672, A340719, A341868, A341870, A341912, A341913.

Sequence in context: A218510 A026816 A008639 * A008633 A347576 A238868

Adjacent sequences: A341911 A341912 A341913 * A341915 A341916 A341917

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2021

Status

approved