%I #6 Aug 06 2021 00:36:23
%S 0,1,1,6,2,6,8,5,0,3,2,7,3,3,6,5,0,0,2,8,7,3,4,0,8,5,0,8,8,7,6,3,0,3,
%T 4,0,0,0,4,5,2,2,3,4,7,0,6,8,9,2,4,2,5,4,9,5,3,7,9,0,2,0,4,5,3,5,6,2,
%U 4,2,0,5,0,2,6,5,7,7,6,0,9,5,0,1,5,0,8,3,9
%N Decimal expansion of 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^5 / (exp(-Pi*x) + exp(Pi*x))^2, negated.
%C Let b(n) = 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^n / (exp(-Pi*x) + exp(Pi*x))^2, then B(s) = Sum_{n>=0} b(n)*s^n/n! = -s*zeta(1 - s) is the Bernoulli function.
%H Peter H. N. Luschny, <a href="https://arxiv.org/abs/2009.06743">An introduction to the Bernoulli function</a>, arXiv:2009.06743 [math.HO], 2020.
%e 0.0116268503273365002873408508876303400045223470689...
%Y Cf. A001620 (n=1), A346833 (n=2), A346833 (n=3), A346834 (n=4), this sequence (n=5), A346836 (n=6).
%K nonn,cons
%O 0,4
%A _Peter Luschny_, Aug 05 2021