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%I #17 Sep 27 2016 10:32:26
%S 180,56700,425675250,390769879500,21438612514068750,
%T 1211517431782539131250,3952575621190533915703125,
%U 28870481903812321637757079687500
%N Denominator of coefficient of Pi^n in Ramanujan-like series for Zeta[4n+3].
%C Sum_{k>0} 1/(tanh(k*Pi)k^(4n-1)) = Pi^(4n-1)*A057866(n)/A057867(n). - _Michael Somos_, Feb 11 2004
%D E. C. Titchmarsh, The Theory of Functions, 2nd ed., Oxford Univ. Press, 1939, p. 135.
%H Seiichi Manyama, <a href="/A057867/b057867.txt">Table of n, a(n) for n = 1..125</a>
%H J. Sondow and E. W. Weisstein, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">MathWorld: Riemann Zeta Function</a>
%e Sum_{k>0} 1/(tanh(k*Pi)k^3) = Pi^3*7/180;
%e Sum_{k>0} 1/(tanh(k*Pi)k^7) = Pi^7*19/56700.
%t 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}]]
%Y Cf. A057866.
%K nonn
%O 1,1
%A _Eric W. Weisstein_
%E Definition corrected by _Tito Piezas III_, May 18 2009
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