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%I #7 Aug 10 2019 04:28:28
%S 1,3,6,4,-3,-22,-23,8,88,139,-19,-472,-869,-101,2684,5668,2104,-15300,
%T -37680,-22428,86645,252383,202936,-482512,-1694944,-1710607,2584008,
%U 11368664,13819803,-12802724,-75911328,-108463344,53647377,503132556,833364427,-127320060
%N Expansion of Sum_{k>=1} mu(k)*log(1 + x^k/(1 - x^k)^4)/k.
%C Inverse Euler transform of tetrahedral numbers (A000292).
%F -1 + Product_{n>=1} 1/(1 - x^n)^a(n) = g.f. of A000292.
%t nmax = 36; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + x^k/(1 - x^k)^4]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t nmax = 50; s = ConstantArray[0, nmax]; Do[s[[j]] = j^2*(j + 1)*(j + 2)/6 - Sum[s[[d]]*(j - d)*(j - d + 1)*(j - d + 2)/6, {d, 1, j - 1}], {j, 1, nmax}]; Table[Sum[MoebiusMu[k/d]*s[[d]], {d, Divisors[k]}]/k, {k, 1, nmax}] (* _Vaclav Kotesovec_, Aug 10 2019 *)
%Y Cf. A000292, A000335, A008683, A308290.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, May 18 2019