OFFSET
0,20
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
FORMULA
T(n,k) = binomial(floor(k/2),n-k)*(-1)^(n-k)
Column k has g.f. x^k*(1-x)^floor(k/2). - Paul Barry, Feb 01 2007
EXAMPLE
Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, -1, 1,
0, 0, 0, -1, 1,
0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 1, -2, 1,
0, 0, 0, 0, 0, 1, -3, 1,
0, 0, 0, 0, 0, 0, 3, -3, 1,
0, 0, 0, 0, 0, 0, -1, 3, -4, 1,
0, 0, 0, 0, 0, 0, 0, -1, 6, -4, 1
MATHEMATICA
Table[(-1)^(n-k)*Binomial[Floor[k/2], n-k], {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Aug 27 2024 *)
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Nov 06 2006
STATUS
approved