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A304448
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Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^2).
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3
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1, 2, 40, 1320, 61984, 3797560, 287566368, 25957422400, 2721948311680, 325260627848442, 43635601119149040, 6494550360714973304, 1062063969900788407680, 189301256401392643093560, 36526821128512112807216192, 7585918627122817713267856320
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 2^(n - 1/2) * exp(n + 1/2) * n^(n - 1/2) / sqrt(Pi).
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MATHEMATICA
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nmax = 20; Table[SeriesCoefficient[Product[((1+x^k)/(1-x^k))^(n^2), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
nmax = 20; Table[SeriesCoefficient[(QPochhammer[-1, x]/2/QPochhammer[x])^(n^2), {x, 0, n}], {n, 0, nmax}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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