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Expansion of Product_{k>=1} (1 - mu(k)*x^k).
2

%I #6 Oct 02 2022 10:29:08

%S 1,-1,1,0,-1,2,-3,3,-2,0,1,-2,2,-2,1,-2,3,-4,4,-2,0,2,-5,6,-5,3,-2,1,

%T -1,1,0,0,3,-6,6,-5,4,0,-5,7,-7,5,-2,2,0,-2,0,1,5,-7,11,-14,11,-6,-1,

%U 9,-12,8,-11,11,-6,10,-13,8,-2,-12,26,-26,24,-20,2,11,-8,14,-15,9

%N Expansion of Product_{k>=1} (1 - mu(k)*x^k).

%t nmax = 75; CoefficientList[Series[Product[(1 - MoebiusMu[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Sum[d MoebiusMu[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]

%Y Cf. A008683, A117208, A185694, A292561, A300663, A306327, A357524, A357525.

%K sign

%O 0,6

%A _Ilya Gutkovskiy_, Oct 02 2022