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A130416
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Numerator of partial sums for a series of (17/18)*Zeta(4) = (17/1680)*Pi^4.
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2
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1, 49, 6623, 741857, 13247611, 3060203141, 13645449045719, 218327192834879, 100212182125865461, 1904031462407822767, 2534265876944902342877, 58288115171766608401171, 128058989033214718801833487
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OFFSET
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1,2
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COMMENTS
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The rationals r(n) = 2*Sum_{k=1..n} 1/(k^4*binomial(2*k,k)) tend, in the limit n->infinity, to (18/17)*Zeta(4) = (17/1680)*Pi^4, approximately 1.022194166.
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REFERENCES
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L. Berggren, T. Borwein and P. Borwein, Pi: A Source Book, Springer, New York, 1997, p. 687.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Exercise.
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LINKS
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FORMULA
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a(n) = numerator(r(n)), n >= 1, with the rationals defined above.
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EXAMPLE
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Rationals: 1, 49/48, 6623/6480, 741857/725760, 13247611/12960000, ...
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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