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A277170
Numerator of 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1).
2
1, -1, 1, -1, 1, -3, 1, -1, 25, -1, 1, -49, 1, -1, 9, -3, 1, -363, 3025, -1, 169, -169, 1, -3, 1, -49, 289, -289, 7225, -361, 361, -361, 1, -1, 1, -529, 529, -529, 330625, -148225, 3025, -675, 9, -3, 7569, -2523, 142129, -409757907, 808201, -961, 8649, -2883, 1, -147
OFFSET
0,6
COMMENTS
Neil Calkin found the closed forms of 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1) in 2007.
REFERENCES
Jonathan Borwein, David Bailey, Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century.
LINKS
FORMULA
(s(n) =) 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1) = a(n) / A277520(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.
MATHEMATICA
a[n_] := HypergeometricPFQ[{3n, -n, n+1}, {2n+1, n+1/2}, 1] // Numerator; Table[a[n], {n, 0, 53}] (* Jean-François Alcover, Oct 22 2016 *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Seiichi Manyama, Oct 19 2016
STATUS
approved