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%I #9 Aug 04 2023 04:35:26
%S 1,2,1,2,2,1,0,0,0,1,0,0,0,2,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T 2,1,0,0,0,0,0,0,2,2,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,
%U 0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A product of Thue-Morse related triangles.
%e Triangle begins:
%e 1;
%e 2, 1;
%e 2, 2, 1;
%e 0, 0, 0, 1;
%e 0, 0, 0, 2, 1;
%e 0, 0, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 2, 1;
%e 0, 0, 0, 0, 0, 0, 2, 2, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e ...
%t T1[n_, k_] := SeriesCoefficient[(1 + ThueMorse[1 + k]*x)*x^k, {x, 0, n}]; (* A127243 *)
%t T2[n_, k_] := Product[ThueMorse[i], {i, k + 1, n}]; (* A127247 *)
%t T[n_, k_] := Sum[T2[n, j]*T1[j, k], {j, 0, n}];
%t Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Aug 04 2023 *)
%Y Product of A127243 with A127247.
%Y Inverse A127251 is given by (-1)^(n+k)T(n,k).
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Jan 10 2007
%E More terms from _Amiram Eldar_, Aug 04 2023
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