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 A138552 #16 Jul 14 2016 03:21:57
%S A138552 1,2,11,90,889,9723,113322,1380522,17382365,224573349,2962117366,
%T A138552 39741658047,540862505806,7450655906450,103713126384420,
%U A138552 1456845308244810,20627719676855685,294136002612344145
%N A138552 Returning walks of length 2n on the upper half of the square lattice, distinct under reflections about the y-axis.
%C A138552 Under reasonable assumptions, a(n)=E[X^{2n}] where the random variable X is the unitarized Frobenius trace X=a_p/sqrt(p) (as p varies) of a genus 2 curve whose Jacobian is isogenous to the product of two elliptic curves, exactly one of which has complex multiplication.
%H A138552 Kiran S. Kedlaya and Andrew V. Sutherland, <a href="http://arXiv.org/abs/0803.4462">Hyperelliptic curves, L-polynomials and random matrices</a>, arXiv:0803.4462 [math.NT], 2008-2010.
%F A138552 a(n) = (A000891(n) + A000108(n))/2.
%F A138552 G.f.: (3*Pi-2*Pi*sqrt(1-4*x)-2*EllipticE(16*x))/(8*Pi*x). - _Benedict W. J. Irwin_, Jul 13 2016
%F A138552 a(n) ~ 16^n*n^(-2)/Pi. - _Ilya Gutkovskiy_, Jul 13 2016
%F A138552 Recurrence: n*(n+1)^2*(3*n - 2)*a(n) = 2*n*(2*n - 1)*(15*n^2 - n - 4)*a(n-1) - 8*(2*n - 3)*(2*n - 1)^2*(3*n + 1)*a(n-2). - _Vaclav Kotesovec_, Jul 14 2016
%e A138552 a(2) = 11 because EEWW, EWEW, EWWE, EWNS, ENSW, ENWS, NEWS, NESW, NSEW, NSNS, NNSS are all the walks of length 4 on the upper half of the square lattice that are distinct under reflections about the y-axis.
%t A138552 CoefficientList[Series[(3 Pi-2 Pi Sqrt[1-4x]-2EllipticE[16 x])/(8Pi x), {x, 0, 20}], x] (* _Benedict W. J. Irwin_, Jul 13 2016 *)
%Y A138552 Cf. A000108, A000891.
%K A138552 nonn
%O A138552 0,2
%A A138552 _Andrew V. Sutherland_, Mar 24 2008