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A277520
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Denominator of 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1).
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2
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1, 3, 25, 147, 1089, 20449, 48841, 312987, 55190041, 14322675, 100100025, 32065374675, 4546130625, 29873533563, 1859904071089, 4089135109921, 9399479144449, 22568149425822049, 1293753708921104809, 2835106739783283, 3289668853728536041
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OFFSET
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0,2
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COMMENTS
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Neil Calkin found the closed forms of 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1) in 2007.
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REFERENCES
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Jonathan Borwein, David Bailey, Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century.
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LINKS
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FORMULA
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(s(n) =) 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1) = A277170(n) / a(n).
s(2k) = (A005810(k) / A066802(k))^2 = (((4k)! * (3k)!) / ((6k)! * k!))^2.
s(2k+1) = -1/3 * (A052203(k) / A187364(k))^2 = -1/3 * (((4k+1)! * (3k)!) / ((6k+1)! * k!))^2.
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MATHEMATICA
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a[n_] := HypergeometricPFQ[{3n, -n, n+1}, {2n+1, n+1/2}, 1] // Denominator;
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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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STATUS
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approved
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