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A146753
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a(n) = denominator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).
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3
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1, 10, 110, 1870, 8602, 249458, 1247290, 51138890, 218502530, 2316126818, 136651482262, 136651482262, 570720896506, 6277929861566, 521068178509978, 46375067887388042, 2016307299451654, 203647037244617054
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OFFSET
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0,2
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COMMENTS
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Previous name was: a(n)=denominator of k_n such that Integrate[(1+x^(3n))/Sqrt[1-x^3],{x,0,1}]= k_n*(Gamma[1/3]^3)/(2^(1/3)Sqrt[3]Pi) where n >= 0.
General formula: Integral_{x=0..1} ((1+x^(3n))/sqrt(1-x^3)) dx = G_3 * k_n = G_3*A146752(n)/A146753(n) = A118292*A146752(n)/A146753(n) where G_3 = (Gamma(1/3)^3)/(2^(1/3)*sqrt(3)*Pi).
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LINKS
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FORMULA
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a(n) = denominator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).
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MATHEMATICA
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Table[Denominator[(1/2) (1 + Product[(2 (1 + 3 k))/(5 + 6 k), {k, 0, n - 1}])], {n, 0, 30}]
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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New name (using given formula) from Joerg Arndt, Sep 24 2022
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STATUS
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approved
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