A127139 Inverse triangle of A126988.

1, -2, 1, -3, 0, 1, 0, -2, 0, 1, -5, 0, 0, 0, 1, 6, -3, -2, 0, 0, 1, -7, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 0, 1, 10, -5, 0, 0, -2, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson, Jan 06 2007

Keywords

• tabl
• sign

Comments

Row sums give A023900.

Left column is A055615.

A127139 * [1, 2, 3, ...] = [1, 0, 0, 0, ...].

A127139 * [1, 0, 0, 0, ...] = A055615.

A127140 is the square of A127139.

Examples

			First few rows of the triangle:
   1;
  -2,  1;
  -3,  0,  1;
   0, -2,  0, 1;
  -5,  0,  0, 0, 1;
   6, -3, -2, 0, 0, 1;
  -7,  0,  0, 0, 0, 0, 1;
  ...
		

Crossrefs

Cf. A126988, A055615, A023900, A127140.

Programs

Mathematica

nn = 10; s = 0; t[1, 1] = 1; t[n_, k_] := t[n, k] = If[k == 1, -Sum[t[n, k + i]/(i + 1)^(s - 1), {i, 1, n - 1}], If[Mod[n, k] == 0, t[n/k, 1], 0], 0]; Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 1, nn}]] (* Mats Granvik, Mar 12 2016 *)

Formula

Inverse triangle of A126988.