OFFSET
0,4
COMMENTS
Row sums are (1,1,0,0,0,.....) with g.f. 1+x. Diagonal sums have g.f. (1-x^2-x^3)/(1-x^3). Product of A114115 and the first difference matrix (1-x,x).
FORMULA
T(n, k) = Sum_{j=0..n} Sum_{i=0..n} C(floor((n+i)/2), j)*C(j, floor((n+i)/2))*(2*C(0, j-k)-C(1, j-k)).
EXAMPLE
Triangle begins
1;
0, 1;
-2, 1, 1;
-1,-1, 1, 1;
0,-2, 0, 1, 1;
0,-1,-1, 0, 1, 1;
0, 0,-2, 0, 0, 1, 1;
0, 0,-1,-1, 0, 0, 1, 1;
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Nov 13 2005
STATUS
approved