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A304461
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Coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^3).
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0
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1, 2, 144, 29232, 12263552, 8807437800, 9671073636672, 15075101792958592, 31660212257148109824, 86182291753025176234602, 295133367252867736074882400, 1241742977667269060006125955952, 6296492342467004634980003629748736, 37869525230334631809014462278624137096
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OFFSET
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0,2
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COMMENTS
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In general, for m>=3, coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^m) is asymptotic to 2^n * n^(m*n) / n!.
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LINKS
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Table of n, a(n) for n=0..13.
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FORMULA
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a(n) ~ 2^(n - 1/2) * exp(n) * n^(2*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^3), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
nmax = 20; Table[SeriesCoefficient[(QPochhammer[-1, x]/2/QPochhammer[x])^(n^3), {x, 0, n}], {n, 0, nmax}]
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CROSSREFS
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Cf. A206623, A270919, A304448, A304459, A304460.
Sequence in context: A282296 A163275 A157073 * A264153 A232998 A103207
Adjacent sequences: A304458 A304459 A304460 * A304462 A304463 A304464
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, May 13 2018
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STATUS
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approved
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