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EXAMPLE
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The table of coefficients of x^k in expansion of Product_{k>=1} ((1 + n*x^k)/(1 - n*x^k))^k begins:
n = 0: (1), 0, 0, 0, 0, 0, ...
n = 1: 1, (2), 6, 16, 38, 88, ...
n = 2: 1, 4, (16), 60, 192, 596, ...
n = 3: 1, 6, 30, (144), 582, 2280, ...
n = 4: 1, 8, 48, 280, (1376), 6568, ...
n = 5: 1, 10, 70, 480, 2790, (15800), ...
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MATHEMATICA
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Table[SeriesCoefficient[Product[((1 + n x^k)/(1 - n x^k))^k, {k, 1, n}], {x, 0, n}], {n, 0, 19}]
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