%I #6 Apr 21 2019 07:50:38

%S 1,2,0,-4,-4,0,4,4,0,-4,0,4,0,-8,-4,8,16,0,-20,-20,8,24,20,-12,-24,-8,

%T 24,4,-16,-24,16,28,24,-40,-32,0,72,24,-28,-104,0,48,88,-44,-32,-64,

%U 92,20,24,-124,64,0,96,-168,-12,-72,272,-24,72,-300,104,-88,316,-272,128,-272,376,-300

%N G.f. A(x) satisfies: (1 + x)/(1 - x) = A(x)*A(x^2)*A(x^3)*A(x^4)* ... *A(x^k)* ...

%C Convolution of A117209 and A117210.

%F G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^mu(k).

%e G.f.: A(x) = 1 + 2*x - 4*x^3 - 4*x^4 + 4*x^6 + 4*x^7 - 4*x^9 + 4*x^11 - 8*x^13 - 4*x^14 + 8*x^15 + ...

%t terms = 67; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^MoebiusMu[k], {k, 1, terms}], {x, 0, terms}], x]

%t terms = 67; A[_] = 1; Do[A[x_] = (1 + x)/((1 - x) Product[A[x^k], {k, 2, terms}]) + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

%Y Cf. A008683, A117209, A117210, A307659.

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, Apr 20 2019