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%I #28 Feb 23 2021 18:02:35
%S 1,1,2,3,5,7,11,15,22,29,40,52,70,89,116,146,186,230,288,352,434,525,
%T 638,764,919,1090,1297,1527,1801,2104,2462,2857,3319,3828,4417,5066,
%U 5811,6630,7563,8588,9747,11018,12447,14012,15760,17674,19798,22122,24688,27493,30573,33940,37616
%N Number of partitions of n into 8 distinct and relatively prime parts.
%F G.f.: Sum_{k>=1} mu(k)* x^(36*k) / Product_{j=1..8} (1 - x^(j*k)).
%t 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] &
%Y Cf. A023022, A023028, A023033, A078374, A101271, A339672, A341868, A341870, A341912, A341913, A341914.
%K nonn
%O 36,3
%A _Ilya Gutkovskiy_, Feb 23 2021