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 A338107 #22 Oct 14 2020 13:54:29
%S A338107 4,0,9,4,4,7,9,2,4,8,9,0,7,6,0,4,0,5,7,5,3,4,1,9,0,1,2,6,9,0,2,5,3,8,
%T A338107 5,0,3,9,5,0,6,8,3,6,6,3,8,8,3,3,8,6,3,3,3,7,0,9,7,0,1,8,2,8,0,1,7,2,
%U A338107 8,5,3,9,7,7,8,8,1,2,5,4,8,5,1,1,5,0,7,0,6,4
%N A338107 Decimal expansion of Sum_{m>1, n>1} 1/(m^2*n^2+1).
%C A338107 Double inequality: Sum_{m>1, n>1} 1/(m^2*n^2+1) = this constant = 0.409... < Sum_{m>1, n>1} 1/(m^2*n^2) = (zeta(2)-1)^2 = 0.415... < Sum_{m>1, n>1} 1/(m^2*n^2-1) = A338106 = 0.423...
%D A338107 Jean-Marie Monier, Analyse, Exercices corrigés, 2ème année MP, Dunod, 1997, Exercice 3.25, p. 277.
%F A338107 Equals Sum_{k>0} (-1)^(k-1) * (zeta(2*k) - 1)^2.
%F A338107 Equals 3/2 - Pi*coth(Pi) + Sum_{k>=1} (Pi*coth(Pi/k)/(2*k) - 1/2). - _Vaclav Kotesovec_, Oct 14 2020
%e A338107 0.40944792489076040575341901269025385039506836638... (with help of _Amiram Eldar_).
%t A338107 RealDigits[Sum[(-1)^(k - 1)*(Zeta[2*k] - 1)^2, {k, 1, 100}], 10, 90][[1]] (* _Amiram Eldar_, Oct 10 2020 *)
%o A338107 (PARI) sumalt(k=1, (-1)^(k-1) * (zeta(2*k) - 1)^2) \\ _Michel Marcus_, Oct 10 2020
%Y A338107 Cf. A098198, A333972, A338106.
%K A338107 nonn,cons
%O A338107 0,1
%A A338107 _Bernard Schott_, Oct 10 2020