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EXAMPLE
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The table of coefficients of x^k in expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(n^k) begins:
n = 0: (1), 0, 0, 0, 0, 0, ...
n = 1: 1, (2), 4, 8, 14, 24, ...
n = 2: 1, 4, (16), 60, 208, 692, ...
n = 3: 1, 6, 36, (200), 1038, 5160 ...
n = 4: 1, 8, 64, 472, (3264), 21608, ...
n = 5: 1, 10, 100, 920, 7950, (65752), ...
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MATHEMATICA
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Table[SeriesCoefficient[Product[((1 + x^k)/(1 - x^k))^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 19}]
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