OFFSET
0,5
COMMENTS
FORMULA
G.f.: Sum_{n>=0, k=0..n} T(n,k)*y^k*x^n=(1+2*(y-1)*x)/((1-2*x)*(1+(y-1)*x)).
|T(2*n,n)| = 4^n = A000302(n).
T(n,k) = (-1)^(k-1) * (Sum_{i=0..n-k} (2^(i+1)-1) * binomial(n-i-1,k-1)) for 0 < k <= n and T(n,0) = 1 for n >= 0. - Werner Schulte, Mar 22 2019
EXAMPLE
Triangle begins:
1;
1, 1;
1, 4, -1;
1, 11, -5, 1;
1, 26, -16, 6, -1;
1, 57, -42, 22, -7, 1;
1, 120, -99, 64, -29, 8, -1;
1, 247, -219, 163, -93, 37, -9, 1;
1, 502, -466, 382, -256, 130, -46, 10, -1;
1, 1013, -968, 848, -638, 386, -176, 56, -11, 1;
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Philippe Deléham, Nov 30 2013
STATUS
approved