%I #5 Sep 19 2018 19:30:32
%S 1,-1,-3,14,-11,-81,282,-57,-2043,5405,2417,-46476,94522,110512,
%T -943407,1505289,2807589,-16888311,23645199,46006542,-265972791,
%U 472882620,187884672,-3981273597,14234579226,-19187383356,-78662039004,502118911904,-847583768679,-2627514175002
%N a(n) = [x^n] Product_{k>=1} ((1 - x^k)*(1 - x^(2*k)))^n.
%F a(n) = [x^n] Product_{k>=1} (1 - x^(2*k))^(2*n)/(1 + x^k)^n.
%F a(n) = [x^n] exp(n*Sum_{k>=1} (sigma(2*k) - 4*sigma(k))*x^k/k).
%t Table[SeriesCoefficient[Product[((1 - x^k) (1 - x^(2 k)))^n , {k, 1, n}], {x, 0, n}], {n, 0, 29}]
%t Table[SeriesCoefficient[(QPochhammer[x] QPochhammer[x^2])^n, {x, 0, n}], {n, 0, 29}]
%t Table[SeriesCoefficient[Exp[n Sum[(DivisorSigma[1, 2 k] - 4 DivisorSigma[1, k]) x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 29}]
%Y Cf. A002171, A002288, A008705, A030204, A030211, A066535, A296043, A296044, A319457.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Sep 19 2018