OFFSET
0,7
COMMENTS
In the Frey-Sellers reference this array is called {n over r}_{m-1}, with m=4.
The step width sequence of this staircase array is [1,3,3,3,....], i.e. the degree of the row polynomials is [0,3,6,9,...]= A008585.
LINKS
D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148.
FORMULA
a(0, 0)=1, a(n, -1)=0, n >= 1; a(n, r)=0 if r>3*n; a(n, r)=a(n, r-1)+a(n-1, r) else.
G.f. for column r=3*k+j, k >= 0, j=1, 2, 3: (x^(k+1))*N(4; k, x)/(1-x)^(3*k+1+j), with the row polynomials N(4; k, x) of array A062751.
EXAMPLE
{1}; {1,1,1,1}; {1,2,3,4,4,4,4}; {1,3,6,10,14,18,22,22,22,22}; ...; N(4; 1,x)=(2-x)*(2-2*x+x^2).
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Jul 12 2001
STATUS
approved