A120918 Row sums of triangle A120914 (cascadence of (1+2x)^2).

1, 12, 124, 1212, 11512, 107544, 994236, 9128024, 83400856, 759387964, 6896903064, 62519804504, 565914425336, 5116780986152, 46223426993576, 417279346904792, 3764890593799336, 33953608251139560, 306100904240342268

Offset: 0

Author

Paul D. Hanna, Jul 17 2006

Keywords

• nonn

Crossrefs

Cf. A120914, A120915, A120916, A120917.

Programs

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))}

Formula

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).