%I #5 Apr 20 2019 08:11:56

%S 1,1,-2,-5,0,4,9,2,-10,-21,29,15,-18,-80,50,59,207,-228,-244,-315,868,

%T 103,360,-1907,752,-151,3802,-5032,965,-5279,13742,-6049,9107,-33835,

%U 25398,-15098,63365,-79614,51752,-117194,196980,-156321,209085,-435223,463497,-441950,871202,-1146187,1023944,-1704179

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

%C Weigh transform of A055615.

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

%e G.f.: A(x) = 1 + x - 2*x^2 - 5*x^3 + 4*x^5 + 9*x^6 + 2*x^7 - 10*x^8 - 21*x^9 + 29*x^10 + 15*x^11 - 18*x^12 - 80*x^13 + ...

%t terms = 49; CoefficientList[Series[Product[(1 + x^k)^(MoebiusMu[k] k), {k, 1, terms}], {x, 0, terms}], x]

%t terms = 49; A[_] = 1; Do[A[x_] = (1 + x)/Product[A[x^k]^k, {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

%Y Cf. A008683, A055615, A117210, A307648.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Apr 19 2019