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A146481
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Decimal expansion of Product_{n>=2} (1 - 1/(n*(n-1))).
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1
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2, 9, 6, 6, 7, 5, 1, 3, 4, 7, 4, 3, 5, 9, 1, 0, 3, 4, 5, 7, 0, 1, 5, 5, 0, 2, 0, 2, 1, 9, 1, 4, 2, 8, 6, 4, 8, 6, 4, 8, 3, 1, 5, 1, 9, 1, 7, 8, 9, 4, 7, 8, 9, 0, 8, 1, 6, 7, 3, 5, 7, 3, 3, 1, 6, 5, 9, 0, 6, 1, 6, 2, 9, 1, 5, 1, 9, 6, 0, 8, 8, 8, 3, 6, 6, 7, 4, 8, 1, 6, 4, 0, 2, 1, 2, 6, 2, 2, 1, 4, 5, 4, 1, 7, 7
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OFFSET
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0,1
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COMMENTS
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Product of Artin's constant A005596 and the equivalent almost-prime products.
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LINKS
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FORMULA
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The logarithm is -Sum_{s>=2} Sum_{j=1..floor(s/(1+r))} binomial(s-r*j-1, j-1)*(1-Zeta(s))/j at r=1.
s*Sum_{j=1..floor(s/2)} binomial(s-j-1, j-1)/j = A001610(s-1).
Equals 1/Product_{k=1..2} Gamma(1-x_k) = -sin(A094886)/A000796, where x_k are the 2 roots of the polynomial x*(x+1)-1. [R. J. Mathar, Feb 20 2009]
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EXAMPLE
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0.2966751347435910345... = (1 - 1/2)*(1 - 1/6)*(1 - 1/12)*(1 - 1/20)*...
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MAPLE
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phi := (1+sqrt(5))/2; evalf(-sin(Pi*phi)/Pi) ; # R. J. Mathar, Feb 20 2009
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MATHEMATICA
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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