A120922 Main diagonal of triangle A120919 (cascadence of (1+x)^3); a(n) = A120919(n,n) for n>=0.

1, 3, 18, 128, 876, 6138, 43373, 307857, 2194731, 15698743, 112614054, 809905638, 5838361138, 42178611879, 305340946455, 2214760026120, 16094665727934, 117171115942752, 854506665035841, 6242259681316251, 45674776431331398

Offset: 0

Author

Paul D. Hanna, Jul 17 2006

Keywords

• nonn

Crossrefs

Cf. A120919, A120920, A120921, A120923.

Programs

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); polcoeff(polcoeff(A,n,x),n,y)}