A057867 Denominator of coefficient of Pi^n in Ramanujan-like series for Zeta[4n+3].

180, 56700, 425675250, 390769879500, 21438612514068750, 1211517431782539131250, 3952575621190533915703125, 28870481903812321637757079687500

Offset

1,1

Comments

Sum_{k>0} 1/(tanh(k*Pi)k^(4n-1)) = Pi^(4n-1)*A057866(n)/A057867(n). - Michael Somos, Feb 11 2004

References

E. C. Titchmarsh, The Theory of Functions, 2nd ed., Oxford Univ. Press, 1939, p. 135.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..125

J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function

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.

Mathematica

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}]]

Crossrefs

Cf. A057866.

Sequence in context: A244056 A091033 A146530 * A075871 A177327 A358413

Adjacent sequences: A057864 A057865 A057866 * A057868 A057869 A057870

Keyword

nonn

Author

Eric W. Weisstein

Extensions

Definition corrected by Tito Piezas III, May 18 2009

Status

approved