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A203692 v(n+1)/v(n), where v=A203691.

%I A203692 #10 Nov 21 2023 07:47:58
%S A203692 13,2709,3024084,11210422275,105517529064567,2124369691794486864,
%T A203692 81235403341710637909248,5408406067938289043927788125,
%U A203692 586601588860841615474452259390625,98362502736855752633918233259787105024
%N A203692 v(n+1)/v(n), where v=A203691.
%C A203692 See A093883 for a discussion and guide to related sequences.
%F A203692 a(n) ~ 3^(3*n/2 + 7/4) * exp(sqrt(3)*Pi*(2*n+3)/4 - 4*n) * n^(4*n) / 2^(2*n). - _Vaclav Kotesovec_, Nov 21 2023
%t A203692 f[j_] := j (j + 1)/2; z = 11;
%t A203692 u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,
%t A203692   {j, 1, k - 1}]
%t A203692 v[n_] := Product[u[n], {k, 2, n}]
%t A203692 Table[v[n], {n, 1, z}]          (* A203691 *)
%t A203692 Table[v[n + 1]/v[n], {n, 1, z}] (* A203692 *)
%t A203692 Table[Product[k^2*(k + 1)^2/4 + k*(k + 1)*(n + 1)*(n + 2)/4 + (n + 1)^2*(n + 2)^2/4, {k, 1, n}], {n, 1, 10}] (* _Vaclav Kotesovec_, Nov 21 2023 *)
%K A203692 nonn
%O A203692 1,1
%A A203692 _Clark Kimberling_, Jan 04 2012