OFFSET
0,3
COMMENTS
In triangle A126470, row n lists coefficients of q in F(n,q) that satisfies: F(n,q) = Sum_{k=0..n-1} C(n-1,k)*F(k,q)*F(n-k-1,q)*q^k for n>0, with F(0,q) = 1.
EXAMPLE
Row functions F(n,q) of triangle A126470 begin:
F(0,q) = F(1,q) = 1;
F(1,q) = 1 + q;
F(2,q) = 1 + 3*q + q^2 + q^3;
F(3,q) = 1 + 6*q + 7*q^2 + 5*q^3 + 3*q^4 + q^5 + q^6.
PROG
(PARI) {F(n, q)=if(n==0, 1, sum(k=0, n-1, binomial(n-1, k)*F(k, q)*F(n-k-1, q)*q^k))} {a(n)=Vec(F(n+1, q)+O(q^(n*(n-1)/2+1)))[n*(n-1)/2+1]}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 31 2006
STATUS
approved