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 A263249 #9 Jul 27 2018 04:32:48
%S A263249 1,-2,-8,112,9088,310528,-14701568,-4554426368,-458243735552,
%T A263249 37024075153408,29290212127670272,6224109737622372352,
%U A263249 -631398107821314670592,-1112417825593218314534912,-422420220419591934719295488,41942640830461258871206838272,165285368668709582104936440659968,101410495525765825487306697440493568
%N A263249 Expansion of e.g.f.: 2*cos(r*x)^2 / (1 + cos(r*x)^2) where r = sqrt(2), even terms only.
%H A263249 G. C. Greubel, <a href="/A263249/b263249.txt">Table of n, a(n) for n = 0..233</a>
%e A263249 E.g.f.: A(x) = 1 - 2*x^2/2! - 8*x^4/4! + 112*x^6/6! + 9088*x^8/8! + 310528*x^10/10! - 14701568*x^12/12! - 4554426368*x^14/14! +...
%t A263249 With[{nn=40},Take[CoefficientList[Series[(2 Cos[x*Sqrt[2]]^2)/(1+Cos[ x*Sqrt[2]]^2),{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Mar 13 2018 *)
%o A263249 (PARI) {a(n) = local(S=x,C=1,D=1,ox=O(x^(2*n+2))); for(i=1,2*n+1, S = intformal(C*D^2 +ox); C = 1 - intformal(S*D^2); D = 1 + intformal(S*C*D);); (2*n)!*polcoeff(C^2, 2*n)}
%o A263249 for(n=0,20,print1(a(n),", "))
%Y A263249 Cf. A263246, A263247, A263248.
%K A263249 sign
%O A263249 0,2
%A A263249 _Paul D. Hanna_, Oct 13 2015