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A258232
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Decimal expansion of Integral_{x=0..1} Product_{k>=1} (1-x^k) dx.
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17
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3, 6, 8, 4, 1, 2, 5, 3, 5, 9, 3, 1, 4, 3, 3, 6, 5, 2, 3, 2, 1, 3, 1, 6, 5, 9, 7, 3, 2, 7, 8, 5, 1, 0, 1, 5, 0, 1, 4, 2, 4, 1, 3, 0, 3, 9, 2, 8, 8, 1, 9, 9, 6, 8, 3, 0, 3, 6, 1, 5, 8, 0, 6, 6, 8, 2, 8, 1, 4, 7, 3, 0, 0, 8, 8, 9, 0, 3, 4, 3, 9, 2, 9, 8, 9, 0, 6, 3, 4, 4, 2, 4, 2, 4, 1, 4, 9, 9, 2, 1, 7, 6, 7, 1, 2, 8
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..105.
Martin Klazar, What is an answer? - remarks, results and problems on PIO formulas in combinatorial enumeration, part I, arXiv:1808.08449 [math.CO], 2018.
Vaclav Kotesovec, The integration of q-series
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FORMULA
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Equals 8*Pi*sqrt(3/23) * sinh(sqrt(23)*Pi/6) / (2*cosh(sqrt(23)*Pi/3) - 1).
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EXAMPLE
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0.3684125359314336523213165973278510150142413039288199683036158...
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MAPLE
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evalf(8*sqrt(3/23)*Pi*sinh(sqrt(23)*Pi/6)/(2*cosh(sqrt(23)*Pi/3)-1), 123);
evalf(Sum((-1)^n/((3*n-1)*n/2 + 1), n=-infinity..infinity), 123);
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MATHEMATICA
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RealDigits[N[8*Sqrt[3/23]*Pi*Sinh[Sqrt[23]*Pi/6] / (2*Cosh[Sqrt[23]*Pi/3]-1), 120]][[1]]
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PROG
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(PARI) 8*Pi*sqrt(3/23) * sinh(sqrt(23)*Pi/6) / (2*cosh(sqrt(23)*Pi/3) - 1) \\ Michel Marcus, Nov 28 2018
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CROSSREFS
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Cf. A010815, A242168, A258229, A258230, A258408.
Cf. A258406 (m=2), A258407 (m=3), A258404 (m=4), A258405 (m=5).
Sequence in context: A200340 A108369 A010621 * A296568 A294095 A306633
Adjacent sequences: A258229 A258230 A258231 * A258233 A258234 A258235
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KEYWORD
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nonn,cons
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AUTHOR
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Vaclav Kotesovec, May 24 2015
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STATUS
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approved
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