A124821 Number triangle T(n,k)=(-1)^(n-k)*(3k+2)*C(3n+1, n-k)/(2n+k+2).

1, -2, 1, 7, -5, 1, -30, 25, -8, 1, 143, -130, 52, -11, 1, -728, 700, -320, 88, -14, 1, 3876, -3876, 1938, -627, 133, -17, 1, -21318, 21945, -11704, 4235, -1078, 187, -20, 1, 120175, -126500, 70840, -27830, 8050, -1700

Offset: 0

Author

Paul Barry, Nov 08 2006

Keywords

• easy
• sign
• tabl

Comments

Inverse of number triangle A124819. Row sums are (-1)^n*A001764(n).

Examples

			Triangle begins
1,
-2, 1,
7, -5, 1,
-30, 25, -8, 1,
143, -130, 52, -11, 1,
-728, 700, -320, 88, -14, 1,
3876, -3876, 1938, -627, 133, -17, 1
		

Links

• Paul Drube, Generalized Path Pairs and Fuss-Catalan Triangles, arXiv:2007.01892 [math.CO], 2020. See Figure 4 p. 8. (up to signs).

Crossrefs

Cf. A124019.