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A292304
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a(n) = [x^n] Product_{k>=1} (1 + n^2*x^k).
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5
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1, 1, 4, 90, 272, 1275, 49284, 124901, 536640, 1620648, 104040100, 223290012, 880969104, 2485978170, 7454471332, 592164776475, 1138401673472, 4109108002310, 10877348160900, 30962024560494, 72270337440400, 7523649856001916, 13202150810778116, 44577985082575400
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OFFSET
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0,3
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LINKS
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FORMULA
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Conjecture: a(n) ~ exp(2*sqrt((Pi^2/6 + 2*log(n)^2)*n)) * (Pi^2/6 + 2*log(n)^2)^(1/4) / (2 * sqrt(Pi) * n^(7/4)).
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MATHEMATICA
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nmax = 30; Table[SeriesCoefficient[Product[(1+n^2*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
Table[SeriesCoefficient[QPochhammer[-n^2, x, 1 + n]/(1 + n^2), {x, 0, n}], {n, 0, 30}]
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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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