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A340719
Number of partitions of n into 8 distinct and relatively prime parts.
6
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
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] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 23 2021
STATUS
approved