A127251 Inverse of number triangle A127249.

1, -2, 1, 2, -2, 1, 0, 0, 0, 1, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Author

Paul Barry, Jan 10 2007

Keywords

• sign
• tabl

Examples

			Triangle begins:
  1;
  -2, 1;
  2, -2, 1;
  0, 0, 0, 1;
  0, 0, 0, -2, 1;
  0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, -2, 1;
  0, 0, 0, 0, 0, 0, 2, -2, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
  ...
		

Crossrefs

Product of A127248 and A127244.

Row sums are A127252.

Cf. A127249.

Programs

Mathematica

T1[n_, k_] := SeriesCoefficient[(1 - ThueMorse[1 + k]*x)*x^k, {x, 0, n}]; (* A127248 *)
T2[n_, k_] := (-1)^(n-k) * Product[ThueMorse[i], {i, k+1, n}]; (* A127244 *)
T[n_, k_] := Sum[T2[n, j]*T1[j, k], {j, 0, n}];
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Amiram Eldar, Aug 04 2023 *)

Extensions

More terms from Amiram Eldar, Aug 04 2023