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Search: id:A146752
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| A146752 |
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a(n)=numerator 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, 7, 71, 1159, 5197, 148025, 730141, 29616293, 125438657, 1319937329, 77390680651, 76972298827, 319946679037, 3504590799071, 289784158718029, 25703039917515461, 1114069690728835, 112203290640603311
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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 denominators of k_n see A146752
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FORMULA
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a(n)=Numerator[(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[Numerator[(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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A146753, A118292
Sequence in context: A067307 A052390 A002119 this_sequence A022518 A113053 A022503
Adjacent sequences: A146749 A146750 A146751 this_sequence A146753 A146754 A146755
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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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