OFFSET
0,3
COMMENTS
The row polynomials Z(2,2; n,y)= sum(a(n,m)*y^m,m=0..n) appear in c(2,2; x) (the g.f. of C(2,2; n) := A064340(n)) with the first (n+1) expansion terms subtracted, as follows: c(2,2; x)-sum(C(2,2; k)*x^k,k=0..n) = x^(n+1)*G(2,2; x)*Z(2,2; n,y), n>=0, where y=c(4*x) and c(x) is the g.f. of A000108 (Catalan) and G(2,2; x) is the g.f. of C(2,2; n+1), that is G(2,2; x)= (c(2,2; x)-1)/x. Hence G(2,2; x)*Z(2,2; k,c(4*x)) is, for k=0,1,..., the g.f. for C(2,2; n+k), n>=0.
FORMULA
a(n, 0)= C(2, 2; n) := A064340(n), n>=0; a(n, 1)= 3*C(2, 2; n), n>=1; a(n, m)=4*sum(a(n-1, k), k=(m-1)..(n-1)) if n>=m>=2, else 0.
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Feb 05 2002
STATUS
approved