A124744 Expansion of (1+x*y)/(1-x^2*y^2+x^3*y^2).
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, 0, 0, 0, 0, 0, 0, 0, 0, -4, 6, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 10, -5, 1
Offset: 0
Examples
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
Links
- Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
Programs
-
Mathematica
Table[(-1)^(n-k)*Binomial[Floor[k/2], n-k], {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Aug 27 2024 *)
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
Comments