A203690 v(n+1)/v(n), where v=A203689.

5, 1480, 204811920, 44845458424326144, 38524837563190678680163123200, 274281830629678279850073754564550983680000000, 30490404582529065278831553253825833486757227887272069693440000000

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 = 8;
u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203689 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203690 *)
Table[Product[k!^2 + (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)