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 A292361 #9 Oct 09 2017 23:33:46
%S A292361 1,3,21,192,2009,22818,273895,3421318,44042729,580473551,7796745921,
%T A292361 106365396629,1470068855112,20543335134692,289818595800636,
%U A292361 4122517765350669,59066177091706608
%N A292361 The number of paths of length 2m in the plane, starting and ending at (0,1), with unit steps in the four directions (north, east, south, west) and staying in the region y > 0 or x > -y.
%H A292361 T. Budd, <a href="https://arxiv.org/abs/1709.04042">Winding of simple walks on the square lattice</a>, arXiv:1709.04042 [math.CO], 2017.
%F A292361 G.f.: A(x) = 1/(2x) - (Pi / (4 x K(16x))) * (1 + 2 Sum_{n>=1} (q^n + 3q^(2n)+ q^(3n)) / (1 + q^n + q^(2n) + q^(3n) + q^(4n)) ), where q=q(16x) is the Jacobi nome of parameter m=16x and K(16x) is the complete elliptic integral of the first kind of parameter m=16x (proven).
%t A292361 a[n_] := SeriesCoefficient[-Pi(1 + 2 Sum[(y+3y^2+y^3)/(1+y+y^2+y^3+y^4) /. y->EllipticNomeQ[m]^l, {l,n+1}])/(4EllipticK[m]) /. m->16x, {x,0,n+1}]
%Y A292361 Cf. A135404.
%K A292361 nonn,walk
%O A292361 0,2
%A A292361 _Timothy Budd_, Sep 15 2017