A124749 Expansion of (1+x*y+x^2*y^2)/(1-x^3*y^3+x^4*y^3).

1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 1

Offset: 0

Author

Paul Barry, Nov 06 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are A124750. Diagonal sums are A124751. Inverse is A124752.

Examples

			Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 0, 1,
0, 0, 0, -1, 1,
0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, -2, 1,
0, 0, 0, 0, 0, 0, 1, -2, 1,
0, 0, 0, 0, 0, 0, 0, 1, -2, 1,
0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 1
		

Crossrefs

Cf. A124744.

Formula

Number triangle T(n,k)=C(floor(k/3),n-k)*(-1)^(n-k)

G.f. of column k is x^k*(1-x)^floor(k/3); - Paul Barry, Dec 14 2006