A203674 v(n+1)/v(n), where v=A203673.

21, 12103, 44121168, 575304812901, 19818489356999424, 1495407279639510367299, 217630534895386228374700032, 55724004016139059166321636355657, 23418841212903851059972098439618560000

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Programs

Mathematica

f[j_] := j^2; z = 12;
u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,
{j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203673 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203674 *)
Table[Product[k^4 + k^2*(n+1)^2 + (n+1)^4, {k, 1, n}], {n, 1, 12}] (* Vaclav Kotesovec, Nov 21 2023 *)

Formula

a(n) ~ 3^(3*n/2 + 1) * exp(sqrt(3)*Pi*(n+1)/2 - 4*n) * n^(4*n). - Vaclav Kotesovec, Nov 21 2023