This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259171 #44 Dec 11 2023 02:43:02
%S A259171 1,0,7,6,6,7,4,0,4,7,4,6,8,5,8,1,1,7,4,1,3,4,0,5,0,7,9,4,7,5,0,0,0,0,
%T A259171 4,9,0,4,4,5,6,5,6,2,6,6,4,0,3,8,1,6,6,6,5,5,7,5,0,6,2,4,8,4,3,9,0,1,
%U A259171 5,4,2,4,7,9,1,8,3,1,0,0,2,1,7,4,3,5
%N A259171 Decimal expansion of Sum_{m>=1} 1/(m^2 + 1).
%C A259171 Essentially the same as A100554 and A113319. - _R. J. Mathar_, Jul 06 2015
%H A259171 Muniru A Asiru, <a href="/A259171/b259171.txt">Table of n, a(n) for n = 1..3000</a>
%H A259171 Junyong Zhao, Shaofang Hong, and Xiao Jiang, <a href="https://arxiv.org/abs/1812.08705">A certain reciprocal power sum is never an integer</a>, arXiv:1812.08705 [math.NT], 2018. See the constant alpha_f.
%F A259171 Equals (Pi*coth(Pi)-1)/2. - _Vaclav Kotesovec_, Jun 27 2015
%F A259171 Equals Integral_{x>=0} sin(x)/(exp(x) - 1) dx. - _Amiram Eldar_, Aug 16 2020
%F A259171 Equals Integral_{x>=0} (sin(x)/sinh(x))^2 dx. - _Amiram Eldar_, Dec 11 2023
%e A259171 1.07667404746858117413405079475000049044565626640381666557
%p A259171 evalf[120]((Pi*coth(Pi)-1)/2); # _Muniru A Asiru_, Dec 21 2018
%t A259171 N[Sum[1/(k^2+1),{k,Infinity}],1000]//RealDigits//First
%o A259171 (PARI) (Pi*cosh(Pi)/sinh(Pi)-1)/2 \\ _Michel Marcus_, Jun 28 2015
%o A259171 (PARI) sumnumrat(1/(x^2+1), 1) \\ _Charles R Greathouse IV_, Jan 20 2022
%Y A259171 Cf. A013661, A259173.
%K A259171 nonn,cons
%O A259171 1,3
%A A259171 _José María Grau Ribas_, Jun 19 2015