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A057866
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Sum_{k>0} 1/(tanh(k*pi) * k^(4n-1)) = Pi^(4n-1)*A057866(n)/A057867(n).
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2
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7, 19, 1453, 13687, 7708537, 4472029801, 149780635937, 11231299844779783, 3688053840923281541, 2659842854283579394387, 1228751826452728351300837, 67537532722660373286810600661
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numerator of coefficient of Pi^n in Ramanujan-like series for zeta(4n-1).
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REFERENCES
| E. C. Titchmarsh, The Theory of Functions, 2nd ed., Oxford Univ. Press, 1939, p. 135. See Example 15.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
| 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
| Numerator[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
| Cf. A057867.
Sequence in context: A107195 A201479 A191624 * A128817 A037005 A022419
Adjacent sequences: A057863 A057864 A057865 * A057867 A057868 A057869
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| Definition revised by N. J. A. Sloane, Sep 20 2009, following a suggestion of Michael Somos, Feb 11 2004
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