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 A096971 #7 Jun 13 2017 22:09:56
%S A096971 1,1,4,13,49,181,685,2605,9988,38479,148879,577930,2249698,8777614,
%T A096971 34315012,134377393,526994773,2069403898,8135377102,32014655626,
%U A096971 126099239329,497083313908,1960943833567,7740893831005,30576064032568
%N A096971 G.f. satisfies: A(x) = A( x^2*A000108(x^2) )*x*A000984(x^2), where A000108(x) is the g.f. for the Catalan sequence and A000984(x) = d/dx x*A000108(x).
%H A096971 R. Resch, F. Stenger and J. Waldvogel, 1996, page 8, <a href="http://e-collection.ethbib.ethz.ch/ecol-pool/incoll/incoll_231.pdf">Functional Equations Related to the Iteration of Functions.</a>
%F A096971 a(n) = Sum_{j=0..[(n+1)/2]} C(2*n-2*j-1, n-1)*a(j), a(0)=a(1)=1. G.f. satisfies: A(x) = A( (1-sqrt(1-4*x^2))/2 )*x/sqrt(1-4*x^2), where A(x) = Sum_{n>=0} a(n)*x^(2*n-1).
%e A096971 A(x) = x^-1 + x + 4*x^3 + 13*x^5 + 49*x^7 + 181*x^9 + 685*x^11 +...
%o A096971 (PARI) a(n)=if(n==0 || n==1,1,sum(j=0,(n+1)\2,binomial(2*n-2*j-1,n-1)*a(j)))
%K A096971 nonn
%O A096971 0,3
%A A096971 _Paul D. Hanna_, Jul 16 2004