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%I #4 Mar 30 2012 18:36:58
%S 1,12,124,1212,11512,107544,994236,9128024,83400856,759387964,
%T 6896903064,62519804504,565914425336,5116780986152,46223426993576,
%U 417279346904792,3764890593799336,33953608251139560,306100904240342268
%N Row sums of triangle A120914 (cascadence of (1+2x)^2).
%F G.f.: A(x) = H(x)*(1-x)/(1-9*x), where H(x) is the g.f. of A120915: H(x) = C(2x)^2*H(x*C(2x)^4) and C(x) is the g.f. of A000108 (Catalan).
%o (PARI) {a(n)=local(A,F=1+4*x+4*x^2,d=2,G=x,H=1+x,S=ceil(log(n+1)/log(d+1))); for(i=0,n,G=x*subst(F,x,G+x*O(x^n)));for(i=0,S,H=subst(H,x,x*G^d+x*O(x^n))*G/x); A=(x*H-y*subst(H,x,x*y^d +x*O(x^n)))/(x*subst(F,x,y)-y); sum(k=0,2*n,polcoeff(polcoeff(A,n,x),k,y))}
%Y Cf. A120914, A120915, A120916, A120917.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 17 2006
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