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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Denominators are given by A130417.
The rationals r(n):=2*sum(1/((k^4)*binomial(2*k,k)),k=1..n) tend, in the limit n->infinity, to (18/17)*Zeta(4) = (17/1680)*Pi^4, approximately 1.022194166.
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REFERENCES
| 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.
A. van der Poorten, A proof that Euler missed..., Math. Intell. 1(1979)195-203; reprinted in Pi: A Source Book, pp. 439-447, footnote 10, p. 446 (conjecture).
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LINKS
| W. Lang, Rationals and limit.
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FORMULA
| a(n)=numerator(r(n)), n>=1, with the rationals defined above.
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EXAMPLE
| Rationals [1, 49/48, 6623/6480, 741857/725760, 13247611/12960000,...].
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CROSSREFS
| Partial sums for Zeta(4): A007410/A007480.
Sequence in context: A053772 A075416 A127861 * A006692 A206247 A180273
Adjacent sequences: A130413 A130414 A130415 * A130417 A130418 A130419
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KEYWORD
| nonn,frac,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
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