OFFSET
0,9
FORMULA
T(n,k) = T(n-1,k-1) + T(n-2,k-1) - T(n-2,k-2), T(0,0)=1, T(n,k) = 0 if k > n or if k < 0.
Sum_{k=0..n} T(n,k)*x^k = (-1)^n*A088139(n+1), A001607(n+1), A000007(n), A000012(n), A099087(n), A190960(n+1) for x = -2, -1, 0, 1, 2, 3 respectively. - Philippe Deléham, Feb 15 2012
G.f.: 1/(1-y*x+y*(y-1)*x^2). - Philippe Deléham, Feb 15 2012
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 0;
0, 0, 2, -1;
0, 0, 1, 1, -1;
0, 0, 0, 3, -2, 0;
0, 0, 0, 1, 3, -4, 1;
0, 0, 0, 0, 4, -2, -2, 1; ...
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Philippe Deléham, Jan 29 2010
STATUS
approved