A346836 Decimal expansion of 2*Pi*Integral_{-oo<=x<=oo} log(1/2 + i*x)^6 / (exp(-Pi*x) + exp(Pi*x))^2, negated.

0, 0, 4, 7, 5, 9, 9, 4, 2, 9, 0, 3, 8, 0, 6, 3, 7, 6, 2, 1, 0, 5, 2, 0, 0, 0, 9, 2, 6, 4, 6, 6, 6, 6, 6, 8, 9, 8, 4, 3, 8, 9, 2, 3, 6, 4, 2, 7, 5, 0, 9, 3, 2, 2, 4, 5, 4, 4, 0, 5, 5, 3, 7, 6, 1, 8, 9, 3, 8, 8, 8, 9, 2, 7, 0, 8, 1, 0, 2, 9, 1, 2, 1, 4, 2, 7, 8, 3, 2

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..88.

Peter H. N. Luschny, An introduction to the Bernoulli function, arXiv:2009.06743 [math.HO], 2020.

Example

0.0047599429038063762105200092646666689843892364275...

Crossrefs

Cf. A001620 (n=1), A346833 (n=2), A346833 (n=3), A346834 (n=4), A346835 (n=5), this sequence (n=6).

Sequence in context: A237198 A248932 A341672 * A046549 A331138 A051544

Adjacent sequences: A346833 A346834 A346835 * A346837 A346838 A346839

Keyword

nonn,cons

Author

Peter Luschny, Aug 05 2021

Status

approved