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 A125279 #3 Mar 30 2012 18:37:01
%S A125279 1,1,3,13,68,400,2555,17375,124280,927711,7189102,57627044,476645965,
%T A125279 4061184195,35604795538,320957712849,2973550524004,28305757130713,
%U A125279 276806230525768,2780528226936569,28686373905833717,303913110837114965
%N A125279 G.f.: A(x) = (1/x)*series_reversion(x^2/G(x)) where G(x) is the g.f. of A030266, which shifts left under self-COMPOSE.
%C A125279 Derived from central terms of triangle: a(n) = A125278(2*n,n)/(n+1).
%F A125279 G.f. satisfies: A(x) = 1 + x*A(x)^2 * A( x^2*A(x)^4/(A(x) - 1) ). By definition, G.f. satisfies: A(x) = 1 + G(x*A(x)^2); G(x*A(x)) = x*A(x)^2; x*A(x^2/G(x)) = G(x); where G(x) = x + x*G(G(x)) is g.f. of A030266.
%e A125279 A(x) = 1 + x + 3*x^2 + 13*x^3 + 68*x^4 + 400*x^5 + 2555*x^6 +...
%e A125279 The g.f. of A030266 is G(x) = x + x*G(G(x)) where
%e A125279 G(x) = x + x^2 + 2*x^3 + 6*x^4 + 23*x^5 + 104*x^6 + 531*x^7 + 2982*x^8+..
%o A125279 (PARI) {a(n)=local(A=1+x);for(i=0,n,A=1+x*A^2*subst(A,x,x^2*A^4/(A-1+x^2*O(x^n)))); polcoeff(A,n,x)}
%Y A125279 Cf. A030266, A125278.
%K A125279 nonn
%O A125279 0,3
%A A125279 _Paul D. Hanna_, Nov 26 2006