A340719 Number of partitions of n into 8 distinct and relatively prime parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 52, 70, 89, 116, 146, 186, 230, 288, 352, 434, 525, 638, 764, 919, 1090, 1297, 1527, 1801, 2104, 2462, 2857, 3319, 3828, 4417, 5066, 5811, 6630, 7563, 8588, 9747, 11018, 12447, 14012, 15760, 17674, 19798, 22122, 24688, 27493, 30573, 33940, 37616

Offset

36,3

Links

Table of n, a(n) for n=36..88.

Formula

G.f.: Sum_{k>=1} mu(k)* x^(36*k) / Product_{j=1..8} (1 - x^(j*k)).

Mathematica

nmax = 88; CoefficientList[Series[Sum[MoebiusMu[k] x^(36 k)/Product[1 - x^(j k), {j, 1, 8}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 36] &

Crossrefs

Cf. A023022, A023028, A023033, A078374, A101271, A339672, A341868, A341870, A341912, A341913, A341914.

Sequence in context: A330640 A319474 A218508 * A026814 A008637 A008631

Adjacent sequences: A340716 A340717 A340718 * A340720 A340721 A340722

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2021

Status

approved