A057866 Sum_{k>=1} 1/(tanh(k*Pi) * k^(4n-1)) = Pi^(4n-1)*A057866(n)/A057867(n).

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

Seiichi Manyama, Table of n, a(n) for n = 1..157

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

Adjacent sequences: A057863 A057864 A057865 * A057867 A057868 A057869

Keyword

nonn

Author

Eric W. Weisstein

Extensions

Definition revised by N. J. A. Sloane, Sep 20 2009, following a suggestion of Michael Somos, Feb 11 2004

Status

approved