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A258229
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Numerator of Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx.
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5
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1, 5, 41, 188, 20777, 126661, 375407075, 4551271607, 2186878968457691, 405572061653677013, 579868609560670025014303, 756499881167742750802544581, 90137667815984749912207449629, 12095883009361301429642260272492831583, 83142433646555338064479023776802561123293
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OFFSET
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1,2
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COMMENTS
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Limit n->infinity a(n) / A258230(n) = limit n->infinity Integral_{x=0..1} Product_{k=1..n} (1-x^k) dx = 8*sqrt(3/23)*Pi*sinh(sqrt(23)*Pi/6) / (2*cosh(sqrt(23)*Pi/3)-1) = A258232 = 0.368412535931433652321316597327851...
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LINKS
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EXAMPLE
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Product_{k=1..n} (1-x^k)
n=1 1 - x
n=2 1 - x - x^2 + x^3
n=3 1 - x - x^2 + x^4 + x^5 - x^6
Integral Product_{k=1..n} (1-x^k) dx
n=1 x - x^2/2
n=2 x - x^2/2 - x^3/3 + x^4/4
n=3 x - x^2/2 - x^3/3 + x^5/5 + x^6/6 - x^7/7
For Integral_{x=0..1} set x=1
n=1 1 - 1/2 = 1/2, a(1) = 1
n=2 1 - 1/2 - 1/3 + 1/4 = 5/12, a(2) = 5
n=3 1 - 1/2 - 1/3 + 1/5 + 1/6 - 1/7 = 41/105, a(3) = 41
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MATHEMATICA
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nmax=15; p=1; Table[p=Expand[p*(1-x^n)]; Total[CoefficientList[p, x]/Range[1, Exponent[p, x]+1]], {n, 1, nmax}] // Numerator
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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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