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Search: id:A057867
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| A057867 |
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Denominator of coefficient of Pi^n in Ramanujan-like series for Zeta[4n+3]. |
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+0
2
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| 180, 56700, 425675250, 390769879500, 21438612514068750, 1211517431782539131250, 3952575621190533915703125, 28870481903812321637757079687500
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Sum_{k>0} 1/(tanh(k*pi)k^(4n-1)) = pi^(4n-1)*A057866(n)/A057867(n) - Michael Somos Feb 11 2004
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REFERENCES
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E. C. Titchmarsh, The Theory of Functions, 2nd ed., Oxford Univ. Press, 1939, p. 135.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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Sum_{k>0} 1/(tanh(k*pi)k^3) = pi^3*7/180, Sum_{k>0} 1/(tanh(k*pi)k^7) = pi^7*19/56700.
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MATHEMATICA
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Denominator[Table[2^(k-1)/(k+1)! Sum[(-1)^(n-1)Binomial[k+1, 2n]BernoulliB[k+1-2n]BernoulliB[2n], {n, 0, (k+1)/2}], {k, 3, 50, 4}]]
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CROSSREFS
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Cf. A057866.
Sequence in context: A035830 A091033 A146530 this_sequence A075871 A074811 A036200
Adjacent sequences: A057864 A057865 A057866 this_sequence A057868 A057869 A057870
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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Definition corrected by Tito Piezas III (tpiezas(AT)gmail.com), May 18 2009
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