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 A129455 #9 Feb 08 2024 01:45:20
%S A129455 1,1,1,1,2,1,1,3,3,1,1,256,384,256,1,1,5,640,640,5,1,1,1146617856,
%T A129455 2866544640,244611809280,2866544640,1146617856,1,1,7,4013162496,
%U A129455 6688604160,6688604160,4013162496,7,1,1,35184372088832,123145302310912,47066867504069920948224,919274755938865643520,47066867504069920948224,123145302310912,35184372088832,1
%N A129455 An analog of Pascal's triangle based on A129454. T(n, k) = A129454(n+1)/(A129454(n-k+1)*A129454(k+1)).
%C A129455 It appears that the T(n,k) are always integers. This would follow from the conjectured prime factorization given in A129454. Calculation suggests that the binomial coefficients C(n,k) divide T(n,k) and that T(n,k)/C(n,k) are perfect sixth powers.
%H A129455 G. C. Greubel, <a href="/A129455/b129455.txt">Rows n = 0..25 of the triangle, flattened</a>
%F A129455 T(n, k) = Product_{h=1..n} Product_{i=1..n} Product_{j=1..n} gcd(h,i,j)/( (Product_{h=1..n-k} Product_{i=1..n-k} Product_{j=1..n-k} gcd(h,i,j))*(Product_{h=1..k} Product_{i=1..k} Product_{j=1..k} gcd(h,i,j)) ).
%F A129455 T(n, n-k) = T(n, k). - _G. C. Greubel_, Feb 07 2024
%e A129455 Triangle starts:
%e A129455 1;
%e A129455 1, 1;
%e A129455 1, 2, 1;
%e A129455 1, 3, 3, 1;
%e A129455 1, 256, 384, 256, 1;
%e A129455 1, 5, 640, 640, 5, 1;
%t A129455 A129454[n_]:= Product[GCD[j,k,m], {j,n-1}, {k,n-1}, {m,n-1}];
%t A129455 A129455[n_, k_]:= A129454[n+1]/(A129454[k+1]*A129454[n-k+1]);
%t A129455 Table[A129455[n,k], {n,0,9}, {k,0,n}]//Flatten (* _G. C. Greubel_, Feb 07 2024 *)
%o A129455 (Magma)
%o A129455 A129454:= func< n | n le 1 select 1 else (&*[(&*[(&*[GCD(GCD(j,k),m): k in [1..n-1]]): j in [1..n-1]]): m in [1..n-1]]) >;
%o A129455 A129455:= func< n,k | A129454(n+1)/(A129454(n-k+1)*A129454(k+1)) >;
%o A129455 [A129455(n,k): k in [0..n], n in [0..9]]; // _G. C. Greubel_, Feb 07 2024
%o A129455 (SageMath)
%o A129455 def A129454(n): return product(product(product(gcd(gcd(j,k),m) for k in range(1,n)) for j in range(1,n)) for m in range(1,n))
%o A129455 def A129455(n,k): return A129454(n+1)/(A129454(n-k+1)*A129454(k+1))
%o A129455 flatten([[A129455(n,k) for k in range(n+1)] for n in range(10)]) # _G. C. Greubel_, Feb 07 2024
%Y A129455 Cf. A092287, A129453, A129454.
%K A129455 nonn,tabl
%O A129455 0,5
%A A129455 _Peter Bala_, Apr 16 2007