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%I #5 Sep 24 2019 12:39:42
%S 1,1,0,2,2,2,3,3,6,7,8,9,14,16,17,26,30,35,43,52,62,77,87,104,133,152,
%T 173,212,251,287,344,397,465,549,627,729,864,986,1127,1325,1524,1740,
%U 2009,2306,2641,3047,3455,3942,4549,5157,5846,6700,7605,8608
%N Expansion of Product_{i>=1, j>=1} 1 / (1 + (-x)^(i*(2*j - 1))).
%F G.f.: Product_{k>=1} 1 / (1 + (-x)^k)^A001227(k).
%t nmax = 53; CoefficientList[Series[Product[1/(1 + (-x)^k)^DivisorSum[k, Mod[#, 2] &], {k, 1, nmax}], {x, 0, nmax}], x]
%t a[n_] := a[n] = If[n == 0, 1, Sum[(-1)^k Sum[(-1)^(k/d) d DivisorSum[d, Mod[#, 2] &], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 53}]
%Y Cf. A001227, A107742, A288007, A327731.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Sep 23 2019