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 A203673 #15 Nov 25 2023 10:57:21 %S A203673 1,21,254163,11213968422384,6451450005117349260375984, %T A203673 127857993263632065817610313129228311433216, %U A203673 191199773886534869435599958788731398661833328276349525268803584 %N A203673 Vandermonde sequence using x^2 + xy + y^2 applied to (1,4,9,...,n^2). %C A203673 See A093883 for a discussion and guide to related sequences. %F A203673 From _Vaclav Kotesovec_, Nov 22 2023: (Start) %F A203673 a(n) = A203012(n) * A203312(n). %F A203673 a(n) ~ c * 3^(n*(3*n+1)/4) * n^(2*n^2 - 2*n - 3/2) / exp(3*n^2 - n*(n+1)*Pi*sqrt(3)/4 - 2*n), where c = Gamma(1/3)^(3/2) * 3^(7/24) * exp(Pi/(8*sqrt(3))) / (2^(5/2) * Pi^(5/2)) = 0.076580853261060033865281896312127877504662138809362419847380161198324... (End) %t A203673 f[j_] := j^2; z = 12; %t A203673 u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2, {j, 1, k - 1}] %t A203673 v[n_] := Product[u[n], {k, 2, n}] %t A203673 Table[v[n], {n, 1, z}] (* A203673 *) %t A203673 Table[v[n + 1]/v[n], {n, 1, z}] (* A203674 *) %Y A203673 Cf. A367550. %K A203673 nonn %O A203673 1,2 %A A203673 _Clark Kimberling_, Jan 04 2012