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A057866 Sum_{k>0} 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 (list; graph; refs; listen; history; text; internal format)
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>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

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 A301808

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

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Last modified September 18 10:11 EDT 2020. Contains 337166 sequences. (Running on oeis4.)