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A203694 v(n+1)/v(n), where v=A203693.

%I A203694 #10 Nov 21 2023 08:18:10
%S A203694 7,837,546364,1193379075,6644086647237,79301495255509072,
%T A203694 1800387492184752516864,71233673448265142887288125,
%U A203694 4594697931876986561881103171875,458419756376283291989575799311713024
%N A203694 v(n+1)/v(n), where v=A203693.
%C A203694 See A093883 for a discussion and guide to related sequences.
%F A203694 a(n) ~ (2 + sqrt(3))^(sqrt(3)*(2*n+3)/2) * exp((Pi/2 - 4)*n + 3*Pi/4) * n^(4*n) / 2^(2*n). - _Vaclav Kotesovec_, Nov 21 2023
%t A203694 f[j_] := j (j + 1)/2; z = 11;
%t A203694 u[n_] := Product[f[j]^2 - f[j] f[k] + f[k]^2,
%t A203694   {j, 1, k - 1}]
%t A203694 v[n_] := Product[u[n], {k, 2, n}]
%t A203694 Table[v[n], {n, 1, z}]          (* A203693 *)
%t A203694 Table[v[n + 1]/v[n], {n, 1, z}] (* A203694 *)
%t A203694 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 A203694 nonn
%O A203694 1,1
%A A203694 _Clark Kimberling_, Jan 04 2012