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A255526
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Coefficient of x^n in Product_{k>=1} 1/(1+x^k)^n.
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13
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-1, 1, -4, 17, -56, 172, -547, 1809, -6061, 20316, -68135, 229244, -774372, 2624119, -8912759, 30328593, -103382254, 352975681, -1206921212, 4132159452, -14163858895, 48601267199, -166930975524, 573872089212, -1974472043081, 6798561779868, -23425506369715
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) ~ (-1)^n * c * d^n / sqrt(n), where d = A318204 = 3.5097543279497033404372735..., c = 0.23322106096789389697797... .
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MATHEMATICA
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Table[SeriesCoefficient[Product[1/(1+x^k)^n, {k, 1, n}], {x, 0, n}], {n, 1, 30}]
(* Calculation of constant c: *) 1/Sqrt[(4 - r^2*s^3*Derivative[0, 2][QPochhammer][-1, r*s])*Pi] /. FindRoot[{QPochhammer[-1, r*s] == 2/s, 2/s + r*s*Derivative[0, 1][QPochhammer][-1, r*s] == 0}, {r, -1/3}, {s, 2}, WorkingPrecision -> 120] (* Vaclav Kotesovec, Oct 03 2023 *)
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CROSSREFS
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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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