A329099 - OEIS

%I #4 Nov 05 2019 01:02:13

%S 1,-1,0,0,1,-2,1,0,2,-4,2,0,4,-10,7,0,7,-23,22,-6,14,-51,59,-24,31,

%T -113,152,-80,66,-244,383,-253,166,-521,930,-746,460,-1133,2219,-2082,

%U 1314,-2494,5208,-5607,3788,-5622,12037,-14608,10830,-13145,27618,-37089,30350,-31914,63248,-92290

%N Expansion of 1 / (1 + Sum_{k>=1} mu(k)^2 * x^k).

%F G.f.: 1 / (1 + Sum_{k>=1} x^A005117(k)).

%t nmax = 55; CoefficientList[Series[1/(1 + Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = -Sum[Boole[SquareFreeQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 55}]

%Y Cf. A002121, A005117, A008683, A280194.

%K sign

%O 0,6

%A _Ilya Gutkovskiy_, Nov 04 2019