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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition revised by N. J. A. Sloane, Sep 20 2009, following a suggestion of Michael Somos, Feb 11 2004
STATUS
approved