A176484 Triangle t(n,m) read by rows: t(n,n)= 1, t(n,m) = (-1)^(n+m)*(m+1), 0<=m

1, -1, 1, 1, -2, 1, -1, 2, -3, 1, 1, -2, 3, -4, 1, -1, 2, -3, 4, -5, 1, 1, -2, 3, -4, 5, -6, 1, -1, 2, -3, 4, -5, 6, -7, 1, 1, -2, 3, -4, 5, -6, 7, -8, 1, -1, 2, -3, 4, -5, 6, -7, 8, -9, 1, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 1

Offset: 0

Author

Roger L. Bagula, Apr 18 2010

Keywords

• sign
• tabl
• easy

Comments

Row sums are 1, 0, 0, -1, -1, -2, -2, -3, -3, -4, -4,..

Obtained from A144328 by deleting the first column, adding a diagonal of +1's, and multiplication with (-1)^(n-m).

Examples

			1;
-1, 1;
1, -2, 1;
-1, 2, -3, 1;
1, -2, 3, -4, 1;
-1, 2, -3, 4, -5, 1;
1, -2, 3, -4, 5, -6, 1;
-1, 2, -3, 4, -5, 6, -7, 1;
1, -2, 3, -4, 5, -6, 7, -8, 1;
-1, 2, -3, 4, -5, 6, -7, 8, -9, 1;
1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 1;
		

Programs

Mathematica

p[x, 0] = 1;
p[x_, n_] := p[x, n] = x^n - Sum[(-1)^(i + Mod[n, 2])*i*x^(i - 1), {i, 1, n}];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]

Formula

t(n,m) = [x^m] (x^n - sum_{j=1..n} (-1)^(j+(n mod 2)) *j*x^(j-1) ) .