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A127244
A Thue-Morse signed falling factorial triangle.
4
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
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
KEYWORD
easy,tabl,sign
AUTHOR
Paul Barry, Jan 10 2007
EXTENSIONS
More terms from Amiram Eldar, Aug 04 2023
STATUS
approved