A203158 v(n+1)/v(n), where v=A203012.

7, 247, 21756, 3613701, 974243088, 388409565699, 214946329538304, 157727064375306153, 148245464311769260800, 173696139110375108022159, 248243987235370949531025408, 425095516929076538387157860013

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; z = 12;
v[n_] := Product[Product[f[j]^2 + f[j] f[k] + f[k]^2,
{j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203012 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203158 *)
Table[Product[k^2 + k*(n+1) + (n+1)^2, {k, 1, n}], {n, 1, 15}] (* Vaclav Kotesovec, Sep 07 2023 *)

Formula

a(n) ~ 3^(3*n/2 + 1) * exp((n+1)*Pi/(2*sqrt(3)) - 2*n) * n^(2*n). - Vaclav Kotesovec, Sep 07 2023