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A318246
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a(n) = [x^n] Product_{k>=1} (1 + 3^n*x^k).
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2
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1, 3, 9, 756, 6642, 118341, 388484100, 10474704297, 564988219686, 22878342156600, 12158489037532504050, 984798697643349485688, 159533936817604246934415, 19383278088136495245171156, 2616739259326831261950662430, 608267042060342812170824926328855679
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OFFSET
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0,2
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COMMENTS
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Conjecture: In general, if m > 1 and a(n) = [x^n] Product_{k>=1} (1 + m^n * x^k), then log(a(n)) ~ log(m)*(sqrt(2)*n^(3/2) - n/2).
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LINKS
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FORMULA
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Conjecture: log(a(n)) ~ log(3)*sqrt(2)*n^(3/2).
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MATHEMATICA
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nmax = 20; Table[SeriesCoefficient[Product[(1+3^n*x^k), {k, 1, n}], {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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