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v(n+1)/v(n), where v=A203673.
2

%I #10 Nov 21 2023 08:55:48

%S 21,12103,44121168,575304812901,19818489356999424,

%T 1495407279639510367299,217630534895386228374700032,

%U 55724004016139059166321636355657,23418841212903851059972098439618560000

%N v(n+1)/v(n), where v=A203673.

%C See A093883 for a discussion and guide to related sequences.

%F a(n) ~ 3^(3*n/2 + 1) * exp(sqrt(3)*Pi*(n+1)/2 - 4*n) * n^(4*n). - _Vaclav Kotesovec_, Nov 21 2023

%t f[j_] := j^2; z = 12;

%t u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,

%t {j, 1, k - 1}]

%t v[n_] := Product[u[n], {k, 2, n}]

%t Table[v[n], {n, 1, z}] (* A203673 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203674 *)

%t Table[Product[k^4 + k^2*(n+1)^2 + (n+1)^4, {k, 1, n}], {n, 1, 12}] (* _Vaclav Kotesovec_, Nov 21 2023 *)

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 04 2012