A138057 Triangle read by rows: row n consists of 0 followed by n (n+1)'s with alternating signs.

0, 0, -2, 0, -3, 3, 0, -4, 4, -4, 0, -5, 5, -5, 5, 0, -6, 6, -6, 6, -6, 0, -7, 7, -7, 7, -7, 7, 0, -8, 8, -8, 8, -8, 8, -8, 0, -9, 9, -9, 9, -9, 9, -9, 9, 0, -10, 10, -10, 10, -10, 10, -10, 10, -10

Offset: 0

Author

Paul Curtz, May 02 2008

Keywords

• tabl
• sign

Examples

			From _Paolo Xausa_, Nov 10 2023: (Start)
Triangle begins:
  n\k|  0   1   2   3   4  ...
  ---+---------------------
   0 |  0;
   1 |  0, -2;
   2 |  0, -3,  3;
   3 |  0, -4,  4, -4;
   4 |  0, -5,  5, -5,  5;
  ... (End)
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1325 (rows 0..50 of the triangle, flattened).

Crossrefs

Cf. A131738.

Programs

Mathematica

Array[Join[{0},(-1)^Range[#](#+1)]&,15,0] (* Paolo Xausa, Nov 10 2023 *)

Formula

T(n,k) = [k>0]*(n+1)*(-1)^k, with n >= 0 and 0 <= k <= n, where [] is the Iverson bracket. - Paolo Xausa, Nov 10 2023