A203686 a(n) = v(n+1)/v(n), where v=A203685.

7, 2236, 285335568, 57547308910500864, 46842899758710033145621708800, 322220837658676800986885694521836421775360000, 34986707114505659359711247628604631290356811281951514165248000000

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn
• easy

Comments

See A093883 for a discussion and guide to related sequences.

Crossrefs

Cf. A203685.

Programs

Mathematica

f[j_] := j!; z = 8;
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}]          (* A203685 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203686 *)
Table[Product[k!^2 + k!*(n+1)! + (n+1)!^2, {k, 1, n}], {n, 1, 10}] (* Vaclav Kotesovec, Nov 21 2023 *)

Formula

From Vaclav Kotesovec, Nov 21 2023: (Start)

a(n) ~ (n+1)!^(2*n).

a(n) ~ (2*Pi)^n * n^(2*n^2 + 3*n) / exp(2*n^2 - 13/6). (End)

Extensions

Definition corrected by Georg Fischer, Nov 25 2021