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 A203686 #15 Nov 21 2023 08:41:06
%S A203686 7,2236,285335568,57547308910500864,46842899758710033145621708800,
%T A203686 322220837658676800986885694521836421775360000,
%U A203686 34986707114505659359711247628604631290356811281951514165248000000
%N A203686 a(n) = v(n+1)/v(n), where v=A203685.
%C A203686 See A093883 for a discussion and guide to related sequences.
%F A203686 From _Vaclav Kotesovec_, Nov 21 2023: (Start)
%F A203686 a(n) ~ (n+1)!^(2*n).
%F A203686 a(n) ~ (2*Pi)^n * n^(2*n^2 + 3*n) / exp(2*n^2 - 13/6). (End)
%t A203686 f[j_] := j!; z = 8;
%t A203686 u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,
%t A203686 {j, 1, k - 1}]
%t A203686 v[n_] := Product[u[n], {k, 2, n}]
%t A203686 Table[v[n], {n, 1, z}] (* A203685 *)
%t A203686 Table[v[n + 1]/v[n], {n, 1, z}] (* A203686 *)
%t A203686 Table[Product[k!^2 + k!*(n+1)! + (n+1)!^2, {k, 1, n}], {n, 1, 10}] (* _Vaclav Kotesovec_, Nov 21 2023 *)
%Y A203686 Cf. A203685.
%K A203686 nonn,easy
%O A203686 1,1
%A A203686 _Clark Kimberling_, Jan 04 2012
%E A203686 Definition corrected by _Georg Fischer_, Nov 25 2021