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 A338856 #8 Nov 12 2020 11:19:05
%S A338856 1,0,8,9,8,6,6,7,3,2,2,9,0,7,4,7,9,3,5,3,2,5,8,0,1,7,9,5,8,0,7,2,9,6,
%T A338856 3,6,0,4,8,5,5,1,6,9,7,7,7,7,8,1,3,6,3,3,9,8,3,1,9,6,0,9,4,7,2,0,7,0,
%U A338856 5,7,8,3,6,7,6,8,3,0,4,4,5,6,1,3,2,4,1,3,2,9,7,9,6,0,2,7,6,2,1,5,6,7,8,2,5
%N A338856 Decimal expansion of Sum_{k>=0} binomial(4*k,2*k)^2 / (2^(8*k) * (2*k + 1)).
%D A338856 Pablo Fernandez Refolio, Problem 12180, The American Mathematical Monthly 127, April 2020, p. 373.
%F A338856 Equals 2/Pi + sqrt(Pi/2) / Gamma(3/4)^2 - sqrt(2) * Gamma(3/4)^2 / Pi^(3/2).
%F A338856 Equals hypergeom([1/4, 1/4, 3/4, 3/4], [1/2, 1, 3/2], 1).
%e A338856 1.0898667322907479353258017958072963604855169777781363398319609472070578367683...
%p A338856 evalf(2/Pi + sqrt(Pi/2) / GAMMA(3/4)^2 - sqrt(2) * GAMMA(3/4)^2 / Pi^(3/2), 120);
%t A338856 RealDigits[2/Pi + Sqrt[Pi/2]/Gamma[3/4]^2 - Sqrt[2]*Gamma[3/4]^2/Pi^(3/2), 10, 100][[1]]
%t A338856 N[HypergeometricPFQ[{1/4, 1/4, 3/4, 3/4}, {1/2, 1, 3/2}, 1], 120]
%Y A338856 Cf. A068465, A276483.
%K A338856 nonn,cons
%O A338856 1,3
%A A338856 _Vaclav Kotesovec_, Nov 12 2020