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 A371802 #16 Mar 29 2025 19:44:48
%S A371802 1,7,4,5,2,6,7,6,9,6,3,3,8,3,9,0,2,5,4,6,1,0,2,6,2,3,5,9,8,9,4,3,3,8,
%T A371802 4,4,8,1,6,2,8,0,3,1,8,5,3,2,8,6,5,0,0,7,2,6,6,9,4,9,0,1,5,4,5,6,3,3,
%U A371802 3,2,9,4,0,1,6,2,1,7,6,9,5,0,8,6,7,8
%N A371802 Decimal expansion of Sum_{k>=0} (-1)^k / (k^2 + 3).
%C A371802 In general, for m > 0, Sum_{k>=0} (-1)^k / (k^2 + m) = 1/(2*m) + Pi * exp(sqrt(m)*Pi) / ((exp(2*sqrt(m)*Pi) - 1) * sqrt(m)). - _Vaclav Kotesovec_, Apr 22 2024
%F A371802 Equals (1/6)*(1 + sqrt(3)*Pi*csch(Pi*sqrt(3))).
%e A371802 0.17452676963383902546102623598943384481...
%t A371802 s = Re[N[Sum[(-1)^k/(k^2 + 3), {k, 0, Infinity}], 120]]
%t A371802 First[RealDigits[s]]
%o A371802 (PARI) sumalt(k=0, (-1)^k / (k^2 + 3)) \\ _Hugo Pfoertner_, Apr 22 2024
%Y A371802 Cf. A329084.
%K A371802 nonn,cons
%O A371802 0,2
%A A371802 _Clark Kimberling_, Apr 17 2024