A155454 Triangle read by rows: t(n,k)= k! + (1-k!)*(n - k)!, 0<=k<=n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, -4, -4, 1, 1, 1, 1, -22, -24, -22, 1, 1, 1, 1, -118, -114, -114, -118, 1, 1, 1, 1, -718, -594, -528, -594, -718, 1, 1, 1, 1, -5038, -3594, -2736, -2736, -3594, -5038, 1, 1, 1, 1, -40318, -25194, -16536, -14160

Offset: 0

Author

Roger L. Bagula, Jan 22 2009

Keywords

• sign
• tabl

Comments

Row sums are 1, 2, 3, 4, 4, -4, -64, -460, -3148, -22732, -178252,...

Examples

			1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 1, 0, 1, 1;
1, 1, -4, -4, 1, 1;
1, 1, -22, -24, -22, 1, 1;
1, 1, -118, -114, -114, -118, 1, 1;
1, 1, -718, -594, -528, -594, -718, 1, 1;
1, 1, -5038, -3594, -2736, -2736, -3594, -5038, 1, 1;
1, 1, -40318, -25194, -16536, -14160, -16536, -25194, -40318, 1, 1;
		

Programs

Mathematica

Table[Table[(k! + (-k + n)! - k!*(n - k)!), {k, 0, n}], {n, 0, 10}];
Flatten[%]