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%I #9 Aug 03 2021 15:29:03
%S 0,0,1,4,10,19,35,52,83,110,165,196,286,329,444,504,680,713,969,1016,
%T 1294,1375,1771,1752,2290,2314,2841,2908,3654,3476,4495,4400,5290,
%U 5304,6500,6124,7770,7467,8852,8688,10660,9802,12341,11700,13652,13409,16215,14768,18389,17190
%N a(n) = Sum_{d|n} mu(n/d) * binomial(d,3).
%F G.f.: Sum_{k>=1} mu(k) * x^(3*k) / (1 - x^k)^4.
%F a(n) = (A059376(n) - 3 * A007434(n) + 2 * A000010(n)) / 6.
%t Table[Sum[MoebiusMu[n/d] Binomial[d, 3], {d, Divisors[n]}], {n, 1, 50}]
%t nmax = 50; CoefficientList[Series[Sum[MoebiusMu[k] x^(3 k)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o (PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(d, 3)); \\ _Michel Marcus_, Aug 03 2021
%Y 3rd column of A020921.
%Y Cf. A000010, A000292, A007434, A059376, A102309, A117108, A346761.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Aug 02 2021
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