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A279226
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Expansion of Product_{k>=1} (1 + x^(k^2))^2.
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8
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1, 2, 1, 0, 2, 4, 2, 0, 1, 4, 5, 2, 0, 4, 8, 4, 2, 6, 7, 4, 5, 8, 6, 4, 4, 10, 15, 8, 1, 12, 24, 12, 1, 8, 19, 18, 10, 8, 16, 24, 17, 16, 23, 20, 12, 22, 34, 20, 8, 20, 42, 38, 18, 18, 42, 52, 30, 20, 34, 46, 34, 30, 46, 48, 36, 46, 72, 58, 33, 42, 71, 72, 41
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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) ~ exp(3 * Pi^(1/3) * ((sqrt(2)-1) * Zeta(3/2))^(2/3) * n^(1/3) / 2) * sqrt(2/3) * ((sqrt(2)-1) * Zeta(3/2) / Pi)^(1/3) / (4*n^(5/6)). - Vaclav Kotesovec, Dec 09 2016
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Product[(1 + x^(k^2))^2, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 20; poly = ConstantArray[0, nmax^2 + 1]; poly[[1]] = 1; poly[[2]] = 2; poly[[3]] = 1; Do[Do[Do[poly[[j + 1]] += poly[[j - k^2 + 1]], {j, nmax^2, k^2, -1}]; , {p, 1, 2}], {k, 2, nmax}]; poly (* Vaclav Kotesovec, Dec 09 2016 *)
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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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