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%I #5 Mar 23 2019 12:38:37
%S 1,1,4,11,33,94,279,803,2348,6823,19879,57834,168405,490125,1426824,
%T 4153197,12089787,35191868,102440785,298194567,868017488,2526715121,
%U 7355031727,21409798576,62321907805,181413177769,528076639862,1537181201003,4474589318797,13025106833162,37914855831345
%N Expansion of 1/(1 - Sum_{k>=1} mu(k)^2*x^k/(1 - x^k)^2).
%C Invert transform of A001615.
%F a(0) = 1; a(n) = Sum_{k=1..n} A001615(k)*a(n-k).
%t nmax = 30; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k/(1 - x^k)^2, {k, 1, nmax}]), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = Sum[DirichletConvolve[j, MoebiusMu[j]^2, j, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]
%Y Cf. A001615, A008683, A156303, A159929, A301594.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 22 2019
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