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 A120916 #3 Mar 30 2012 18:36:58
%S A120916 1,2,8,42,244,1504,9656,63856,431872,2972778,20756036,146627648,
%T A120916 1046060836,7525452296,54530660832,397628393728,2915496099136,
%U A120916 21481907631872,158975372309176,1181109256858096,8806197969093184
%N A120916 G.f. satisfies: A(x) = C(2x)*A(x^3*C(2x)^4), where C(x) is the g.f. of the Catalan numbers (A000108).
%C A120916 Self-convolution equals A120915, which equals column 0 of triangle A120914 (cascadence of (1+2x)^2).
%o A120916 (PARI) {a(n)=local(A=1+2*x,C=(1/x*serreverse(x/(1+4*x+4*x^2+x*O(x^n))))^(1/2)); for(i=0,n,A=C*subst(A,x,x^3*C^4 +x*O(x^n)));polcoeff(A,n,x)}
%Y A120916 Cf. A120914, A120915, A000108.
%K A120916 nonn
%O A120916 0,2
%A A120916 _Paul D. Hanna_, Jul 17 2006