A127247 A Thue-Morse 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

Comments

Central coefficients are C(1,n).

Links

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

Formula

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

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_] := 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 is A127248.

Signed version is A127244.

Row sums are A127246.

Cf. A010060.

Sequence in context: A127507 A204441 A127244 * A144778 A143142 A174856

Adjacent sequences: A127244 A127245 A127246 * A127248 A127249 A127250

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 10 2007

Extensions

More terms from Amiram Eldar, Aug 04 2023

Status

approved