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A050970
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Numerator of S(n)/Pi^n, where S(n) = Sum((4k+1)^(-n),k,-inf,+inf).
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5
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1, 1, 1, 1, 5, 1, 61, 17, 277, 31, 50521, 691, 540553, 5461, 199360981, 929569, 3878302429, 3202291, 2404879675441, 221930581, 14814847529501, 4722116521, 69348874393137901, 56963745931, 238685140977801337, 14717667114151
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Reduced numerators of Favard constants.
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REFERENCES
| 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
| 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
| There is a simple formula in terms of Euler and Bernoulli numbers.
a(2n) = A046976(n), a(2n+1) = A089171(n+1) (conjectured).
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EXAMPLE
| 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
| Denominators: A068205. See also A050971.
Cf. A046982.
Sequence in context: A144342 A144268 A013988 * A138548 A113114 A099740
Adjacent sequences: A050967 A050968 A050969 * A050971 A050972 A050973
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KEYWORD
| nonn,frac
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Mar 24, 2002
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