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%I #4 Mar 30 2012 18:36:58
%S 1,10,89,755,6261,51276,416802,3371901,27192291,218814309,1758106311,
%T 14110481670,113160495179,906973579067,7266174714391,58193602100496,
%U 465947698757267,3730070760926851,29856161486307842,238947353750059666
%N Row sums of triangle A120919 (cascadence of (1+x)^3).
%F G.f.: A(x) = H(x)*(1-x)/(1-8*x), where H(x) is g.f. of A120920: H(x) = G*H(x^4*G^3) and G(x) is g.f. of A001764: G(x) = 1 + x*G(x)^3.
%o (PARI) {a(n)=local(A,F=(1+x)^3,d=3,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=0,3*n,polcoeff(polcoeff(A,n,x),k,y))}
%Y Cf. A120919, A120920, A120921, A120922; A001764 (ternary trees).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 17 2006
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