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

0,1

Links

Table of n, a(n) for n=0..90.

Formula

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

Example

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;
  ...

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 *)

Crossrefs

Inverse of A127243.

Row sums are A127245.

Cf. A010060.

Sequence in context: A152614 A127507 A204441 * A127247 A144778 A143142

Adjacent sequences: A127241 A127242 A127243 * A127245 A127246 A127247

Keyword

easy,tabl,sign

Author

Paul Barry, Jan 10 2007

Extensions

More terms from Amiram Eldar, Aug 04 2023

Status

approved