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A261520
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Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(3^k).
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8
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1, 6, 36, 200, 1038, 5160, 24776, 115632, 527172, 2355998, 10349448, 44783064, 191211512, 806737800, 3367294320, 13918479872, 57020736942, 231697484304, 934399998412, 3742041461976, 14888854356840, 58881590423856, 231542984619720, 905666813058384
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OFFSET
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0,2
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COMMENTS
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In general, for m > 1, if g.f. = Product_{k>=1} ((1+x^k)/(1-x^k))^(m^k), then a(n) ~ m^n * exp(2*sqrt(2*n) - 1 + c) / (sqrt(Pi) * 2^(3/4) * n^(3/4)), where c = 2 * Sum_{j>=1} 1/((2*j+1)*(m^(2*j)-1)).
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LINKS
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FORMULA
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a(n) ~ 3^n * exp(2*sqrt(2*n) - 1 + c) / (sqrt(Pi) * 2^(3/4) * n^(3/4)), where c = 2 * Sum_{j>=1} 1/((2*j+1)*(3^(2*j)-1)) = 0.0887630729103166089354170592729856346...
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(3^k), {k, 1, nmax}], {x, 0, nmax}], x]
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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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