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

Author

Paul Barry, Nov 06 2006

Keywords

• easy
• sign
• tabl

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).

Crossrefs

Cf. A124745 (row sums), A124746 (diagonal sums), A124747 (inverse).

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