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A329069
Expansion of Product_{k>=1} 1 / (1 + mu(k)^2 * x^k).
1
1, -1, 0, -1, 2, -2, 1, -2, 4, -3, 2, -4, 7, -6, 4, -8, 12, -10, 9, -14, 20, -18, 16, -24, 32, -29, 27, -38, 49, -46, 43, -59, 74, -71, 69, -90, 112, -107, 106, -136, 164, -160, 159, -199, 238, -232, 234, -288, 338, -333, 338, -412, 477, -473, 485, -582, 667, -666, 686, -813, 923
OFFSET
0,5
COMMENTS
Convolution inverse of A087188.
FORMULA
G.f.: Product_{k>=1} 1 / (1 + x^A005117(k)).
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[1/(1 + MoebiusMu[k]^2 x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d) Boole[SquareFreeQ[d]] d, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 60}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 04 2019
STATUS
approved