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A057866
Sum_{k>=1} 1/(tanh(k*Pi) * k^(4n-1)) = Pi^(4n-1)*A057866(n)/A057867(n).
4
7, 19, 1453, 13687, 7708537, 4472029801, 149780635937, 11231299844779783, 3688053840923281541, 2659842854283579394387, 1228751826452728351300837, 67537532722660373286810600661
OFFSET
1,1
COMMENTS
Numerator of coefficient of Pi^n in Ramanujan-like series for zeta(4n-1).
REFERENCES
E. C. Titchmarsh, The Theory of Functions, 2nd ed., Oxford Univ. Press, 1939, p. 135. See Example 15.
LINKS
J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function
EXAMPLE
Sum_{k>=1} 1/(tanh(k*Pi)k^3) = Pi^3*7/180,
Sum_{k>=1} 1/(tanh(k*Pi)k^7) = Pi^7*19/56700.
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}]]
CROSSREFS
Cf. A057867.
Sequence in context: A330875 A330852 A267237 * A329001 A334982 A339698
KEYWORD
nonn
EXTENSIONS
Definition revised by N. J. A. Sloane, Sep 20 2009, following a suggestion of Michael Somos, Feb 11 2004
STATUS
approved