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 A102558 #18 Jun 05 2025 23:31:53
%S A102558 3,9,27,837,891,729,12393,277749,4782969,91703097,92293587,82019061,
%T A102558 2674388259,10722885057,155747819547,19336668383673,667382013477,
%U A102558 1019303306559,716912704223253,717162977859147,29411190301301847
%N A102558 Numerator of the probability that (2n+1)-dimensional Gaussian random triangle has an obtuse angle.
%H A102558 G. C. Greubel, <a href="/A102558/b102558.txt">Table of n, a(n) for n = 1..1000</a>
%H A102558 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GaussianTrianglePicking.html">Gaussian Triangle Picking</a>
%F A102558 From _G. C. Greubel_, Feb 01 2025: (Start)
%F A102558 a(n) = numerator( p(n) ), where p(n) = Pi/sqrt(3) - (3^(n+1)/(2*binomial(2*n, n))) * Sum_{k>=0} binomial(2*k, k)*(3/16)^k/(2*k + 2*n + 1).
%F A102558 a(n) = numerator( p(n) ), where p(n) = Pi/sqrt(3) - (3^(n+1)/(2*(2*n+1)*binomial(2*n,n))) * Hypergeometric2F1([1/2, 1/2 + n], [3/2+n], 3/4). (End)
%e A102558 1 - (3*sqrt(3))/(4*Pi), 1 - (9*sqrt(3))/(8*Pi), 1 - (27*sqrt(3))/(20*Pi), ...
%t A102558 Table[Numerator[Simplify[Pi/Sqrt[3] - 3^(n+1)*Hypergeometric2F1[1/2, 1/2 + n, 3/2+n, 3/4]/(2*(2*n+1)*Binomial[2*n,n])]], {n,40}] (* _G. C. Greubel_, Feb 01 2025 *)
%Y A102558 Cf. A102556, A102557, A102559 (denominator).
%K A102558 nonn,frac
%O A102558 1,1
%A A102558 _Eric W. Weisstein_, Jan 14 2005