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 A215128 #13 Aug 04 2012 13:30:01
%S A215128 1,2,12,64,370,2184,13132,79944,491238,3040400,18926336,118369368,
%T A215128 743199184,4681668488,29574616440,187281906512,1188494457492,
%U A215128 7556371963488,48123031011036,306929964849200,1960230225450420,12534313062502440,80236414444623240
%N A215128 G.f.: Sum_{n>=0} d^n/dx^n (x + x^2)^(2*n) / n!.
%C A215128 Compare to: Sum_{n>=0} d^n/dx^n x^(2*n)/n! = 1/sqrt(1-4*x).
%F A215128 a(n) = (n+1)*A214372(n+1), where G(x) = x + (G(x) + G(x)^2)^2 is the g.f. of A214372.
%e A215128 G.f.: A(x) = 1 + 2*x + 12*x^2 + 64*x^3 + 370*x^4 + 2184*x^5 + 13132*x^6 +...
%e A215128 such that, by definition:
%e A215128 A(x) = 1 + d/dx (x+x^2)^2 + d^2/dx^2 (x+x^2)^4/2! + d^3/dx^3 (x+x^2)^6/3! + d^4/dx^4 (x+x^2)^8/4! + d^5/dx^5 (x+x^2)^10/5! +...
%o A215128 (PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}
%o A215128 {a(n)=local(A=x); A=1+sum(m=1, n, Dx(m, x^(2*m)*(1+x+x*O(x^n))^(2*m)/m!)); polcoeff(A, n)}
%o A215128 for(n=0, 25, print1(a(n), ", "))
%Y A215128 Cf. A214372, A215125, A215129, A038112.
%K A215128 nonn
%O A215128 0,2
%A A215128 _Paul D. Hanna_, Aug 04 2012