A127244 A Thue-Morse signed falling factorial triangle.

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

Offset: 0

Author

Paul Barry, Jan 10 2007

Keywords

• easy
• tabl
• sign

Examples

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

Crossrefs

Inverse of A127243.

Row sums are A127245.

Cf. A010060.

Programs

Mathematica

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

Formula

T(n,k) = (-1)^(n-k) * Product_{j=0..n-k-1} A010060(n-j) * [k<=n].

Extensions

More terms from Amiram Eldar, Aug 04 2023