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 A127253 #7 Aug 04 2023 04:35:43
%S A127253 1,0,1,-1,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T A127253 0,1,0,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,
%U A127253 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A127253 Product of number triangles A127243 and A127248.
%C A127253 Rows containing -1 entries are indexed by twice the odious numbers given by A091855.
%e A127253 Triangle begins:
%e A127253 1;
%e A127253 0, 1;
%e A127253 -1, 0, 1;
%e A127253 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 0, 0, -1, 0, 1;
%e A127253 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127253 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A127253 ...
%t A127253 T1[n_, k_] := SeriesCoefficient[(1 + ThueMorse[1 + k]*x)*x^k, {x, 0, n}]; (* A127243 *)
%t A127253 T2[n_, k_] := SeriesCoefficient[(1 - ThueMorse[1 + k]*x)*x^k, {x, 0, n}]; (* A127248 *)
%t A127253 T[n_, k_] := Sum[T2[n, j]*T1[j, k], {j, 0, n}];
%t A127253 Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Aug 04 2023 *)
%Y A127253 Row sums are A127254.
%Y A127253 Cf. A000069, A091855, A127243, A127248.
%K A127253 sign,tabl
%O A127253 0,1
%A A127253 _Paul Barry_, Jan 10 2007