This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A127244 #9 Aug 04 2023 04:34:58
%S A127244 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,
%T A127244 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,
%U A127244 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
%N A127244 A Thue-Morse signed falling factorial triangle.
%F A127244 T(n,k) = (-1)^(n-k) * Product_{j=0..n-k-1} A010060(n-j) * [k<=n].
%e A127244 Triangle begins:
%e A127244 1;
%e A127244 -1, 1;
%e A127244 1, -1, 1;
%e A127244 0, 0, 0, 1;
%e A127244 0, 0, 0, -1, 1;
%e A127244 0, 0, 0, 0, 0, 1;
%e A127244 0, 0, 0, 0, 0, 0, 1;
%e A127244 0, 0, 0, 0, 0, 0, -1, 1;
%e A127244 0, 0, 0, 0, 0, 0, 1, -1, 1;
%e A127244 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127244 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127244 ...
%t A127244 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 *)
%Y A127244 Inverse of A127243.
%Y A127244 Row sums are A127245.
%Y A127244 Cf. A010060.
%K A127244 easy,tabl,sign
%O A127244 0,1
%A A127244 _Paul Barry_, Jan 10 2007
%E A127244 More terms from _Amiram Eldar_, Aug 04 2023