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Search: id:A146753
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| A146753 |
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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=0,1,2,... |
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+0
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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COMMENT
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General formula (*Artur Jasinski*): Integrate[(1+x^(3n))/Sqrt[1-x^3],{x,0,1}] = G_3 * k_n =
G_3*A146751(n)/A146752(n) = A118292*A146751(n)/A146752(n
where G_3 = (Gamma[1/3]^3)/(2^(1/3)Sqrt[3]Pi)
For constant G_3 see A118292
For numerators of k_n see A146752
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FORMULA
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a(n)=Denominator[(1/2) (1 + Product[(2 (1 + 3 k))/(5 + 6 k), {k, 0, n - 1}]
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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}] (*Artur Jasinski*)
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CROSSREFS
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A146752, A118292
Sequence in context: A055530 A108487 A099883 this_sequence A020767 A036603 A092500
Adjacent sequences: A146750 A146751 A146752 this_sequence A146754 A146755 A146756
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Nov 01 2008
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