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 A129453 #9 Feb 07 2024 02:56:48
%S A129453 1,1,1,1,2,1,1,3,3,1,1,16,24,16,1,1,5,40,40,5,1,1,864,2160,11520,2160,
%T A129453 864,1,1,7,3024,5040,5040,3024,7,1,1,2048,7168,2064384,645120,2064384,
%U A129453 7168,2048,1,1,729,746496,1741824,94058496,94058496,1741824,746496,729,1
%N A129453 An analog of Pascal's triangle based on A092287. T(n,k) = A092287(n)/(A092287(n-k)*A092287(k)), 0 <= k <= n.
%C A129453 It appears that the T(n,k) are always integers. This would follow from the conjectured prime factorization given in A092287. Calculation suggests that the binomial coefficients C(n,k) divide T(n,k) and indeed that T(n,k)/C(n,k) are perfect squares.
%H A129453 G. C. Greubel, <a href="/A129453/b129453.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A129453 T(n, k) = (Product_{i=1..n} Product_{j=1..n} gcd(i,j)) / ( (Product_{i=1..n-k} Product_{j=1..n-k} gcd(i,j)) * ( Product_{i=1..k} Product_{j=1..k} gcd(i,j)) ), note that empty products equal to 1.
%F A129453 T(n, n-k) = T(n, k). - _G. C. Greubel_, Feb 07 2024
%e A129453 Triangle starts:
%e A129453 1;
%e A129453 1, 1;
%e A129453 1, 2, 1;
%e A129453 1, 3, 3, 1;
%e A129453 1, 16, 24, 16, 1;
%e A129453 1, 5, 40, 40, 5, 1;
%t A129453 A092287[n_]:= Product[GCD[j,k], {j,n}, {k,n}];
%t A129453 A129453[n_, k_]:= A092287[n]/(A092287[k]*A092287[n-k]);
%t A129453 Table[A129453[n, k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Feb 07 2024 *)
%o A129453 (Magma)
%o A129453 A092287:= func< n | n eq 0 select 1 else (&*[(&*[GCD(j,k): k in [1..n]]): j in [1..n]]) >;
%o A129453 A129453:= func< n,k | A092287(n)/(A092287(n-k)*A092287(k)) >;
%o A129453 [A129453(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Feb 07 2024
%o A129453 (SageMath)
%o A129453 def A092287(n): return product(product( gcd(j,k) for k in range(1,n+1)) for j in range(1,n+1))
%o A129453 def A129453(n,k): return A092287(n)/(A092287(n-k)*A092287(k))
%o A129453 flatten([[A129453(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Feb 07 2024
%Y A129453 Cf. A007318, A092287, A129454, A129455.
%K A129453 nonn,tabl
%O A129453 0,5
%A A129453 _Peter Bala_, Apr 16 2007