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%I #4 Oct 28 2019 20:05:53
%S 1,3,1,3,-3,2,-1,4,3,-8,-1,6,3,-4,-7,12,1,-6,7,0,-13,-13,27,13,-19,
%T -11,11,-21,-25,191,-81,-300,89,327,325,-745,-275,579,-255,1287,-453,
%U -2075,-583,2142,5985,-6698,-6661,6981,3045,3857,-7205,-2784,-5447,-4891,48547
%N Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} sigma(n) * x^n, where sigma = A000203.
%C Inverse weigh transform of A000203.
%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = DivisorSigma[1, n] - b[n, n - 1]; Array[a, 55]
%Y Cf. A000203, A192065, A320780.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Oct 27 2019