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 A127247 #7 Aug 04 2023 04:35:15
%S A127247 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,
%T A127247 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,
%U A127247 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A127247 A Thue-Morse falling factorial triangle.
%C A127247 Central coefficients are C(1,n).
%F A127247 T(n,k) = [k<=n] * Product_{j=0..n-k-1} A010060(n-j).
%e A127247 Triangle begins:
%e A127247 1;
%e A127247 1, 1;
%e A127247 1, 1, 1;
%e A127247 0, 0, 0, 1;
%e A127247 0, 0, 0, 1, 1;
%e A127247 0, 0, 0, 0, 0, 1;
%e A127247 0, 0, 0, 0, 0, 0, 1;
%e A127247 0, 0, 0, 0, 0, 0, 1, 1;
%e A127247 0, 0, 0, 0, 0, 0, 1, 1, 1;
%e A127247 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127247 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127247 ...
%t A127247 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 *)
%Y A127247 Inverse is A127248.
%Y A127247 Signed version is A127244.
%Y A127247 Row sums are A127246.
%Y A127247 Cf. A010060.
%K A127247 easy,nonn,tabl
%O A127247 0,1
%A A127247 _Paul Barry_, Jan 10 2007
%E A127247 More terms from _Amiram Eldar_, Aug 04 2023