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A291748
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Expansion of Product_{k>=1} (1 + x^(2*k^2 - 1)).
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2
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1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0
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OFFSET
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0,50
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LINKS
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FORMULA
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a(n) ~ exp(3 * Pi^(1/3) * ((sqrt(2)-1) * Zeta(3/2))^(2/3) * n^(1/3)/4) * ((sqrt(2)-1) * Zeta(3/2))^(1/3) / (2 * sqrt(6) * Pi^(1/3) * n^(5/6)).
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MATHEMATICA
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nmax = 200; CoefficientList[Series[Product[(1 + x^(2*k^2 - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[Do[poly[[j + 1]] += poly[[j - 2*k^2 + 2]], {j, nmax, 2*k^2 - 1, -1}]; , {k, 2, Sqrt[(nmax + 1)/2] + 1}]; poly
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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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