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Search: id:A050971
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| A050971 |
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4*Denominator of S(n)/Pi^n, where S(n) = Sum((4k+1)^(-n),k,-inf,+inf). |
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3
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| 1, 2, 8, 24, 384, 240, 46080, 40320, 2064384, 725760, 3715891200, 159667200, 392398110720, 12454041600, 1428329123020800, 20922789888000, 274239191619993600, 711374856192000, 1678343852714360832000
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OFFSET
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1,2
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COMMENT
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Reduced denominators of the Favard constants.
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REFERENCES
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N. D. Elkies, On the sums Sum_{k = -infinity .. infinity} (4k+1)^(-n), Amer. Math. Monthly, 110 (No. 7, 2003), 561-573.
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LINKS
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N. D. Elkies, On the sums Sum((4k+1)^(-n),k,-inf,+inf)
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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There is a simple formula in terms of Euler and Bernoulli numbers.
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EXAMPLE
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The first few values of S(n)/Pi^n are 1/4, 1/8, 1/32, 1/96, 5/1536, 1/960, ...
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CROSSREFS
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Cf. A068205. Numerators: A050970.
Sequence in context: A071599 A047695 A093842 this_sequence A118855 A009515 A070944
Adjacent sequences: A050968 A050969 A050970 this_sequence A050972 A050973 A050974
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KEYWORD
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nonn,frac
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Mar 24, 2002
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