A120923 Row sums of triangle A120919 (cascadence of (1+x)^3).

1, 10, 89, 755, 6261, 51276, 416802, 3371901, 27192291, 218814309, 1758106311, 14110481670, 113160495179, 906973579067, 7266174714391, 58193602100496, 465947698757267, 3730070760926851, 29856161486307842, 238947353750059666

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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.

Prog

(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))}

Crossrefs

Cf. A120919, A120920, A120921, A120922; A001764 (ternary trees).

Sequence in context: A269008 A000826 A282555 * A057081 A024132 A192898

Adjacent sequences: A120920 A120921 A120922 * A120924 A120925 A120926

Keyword

nonn

Author

Paul D. Hanna, Jul 17 2006

Status

approved