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Search: id:A068205
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| A068205 |
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Denominator of S(n)/Pi^n, where S(n) = Sum((4k+1)^(-n),k,-inf,+inf). |
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+0
3
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| 4, 8, 32, 96, 1536, 960, 184320, 161280, 8257536, 2903040, 14863564800, 638668800, 1569592442880, 49816166400, 5713316492083200, 83691159552000, 1096956766479974400, 2845499424768000, 6713375410857443328000
(list; graph; listen)
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OFFSET
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1,1
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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)
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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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Numerators: A050970.
Adjacent sequences: A068202 A068203 A068204 this_sequence A068206 A068207 A068208
Sequence in context: A094015 A094867 A086344 this_sequence A113479 A103970 A034785
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KEYWORD
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nonn,frac
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AUTHOR
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njas, Mar 24 2002
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