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A303387
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Expansion of Product_{k>=1} ((1 - 4*x^k)/(1 + 4*x^k))^(1/4).
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5
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1, -2, 0, -10, 22, -102, 244, -1270, 3360, -16886, 46160, -230670, 656550, -3238250, 9474684, -46289530, 138590342, -671116710, 2047182480, -9837322110, 30482926482, -145474988978, 456854466860, -2166890174370, 6884188144964, -32471461699594
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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) ~ c * (-4)^n / n^(3/4), where c = (QPochhammer[-1, -1/4] / QPochhammer[-1/4])^(1/4) / Gamma(1/4) = 0.29599817925108933574246285.... - Vaclav Kotesovec, Apr 25 2018
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MAPLE
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seq(coeff(series(mul(((1-4*x^k)/(1+4*x^k))^(1/4), k = 1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 23 2018
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-4*x^k)/(1+4*x^k))^(1/4)))
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CROSSREFS
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Expansion of Product_{k>=1} ((1 - 2^b*x^k)/(1 + 2^b*x^k))^(1/(2^b)): A002448 (b=0), A303345 (b=1), this sequence (b=2), A303396 (b=3).
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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