%I
%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
