%I #9 Nov 21 2023 05:33:09

%S 1,5,7400,1515608208000,67968144879431450715389952000,

%T 2618461740951506934762583974466059060153960058218086400000

%N Vandermonde sequence using x^2 + y^2 applied to (1,2,6,...,n!).

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

%F a(n) ~ c * n^(2*n^3/3 + n^2/2 - 7*n/6 - 3/4) * (2*Pi)^(n*(n-1)/2) / exp(8*n^3/9 - n^2/4 - 2*n), where c = 0.574053995428296820717722993471497472923951255369819486673614046900594637219... - _Vaclav Kotesovec_, Nov 21 2023

%t f[j_] := j!; z = 8;

%t u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]

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

%t Table[v[n], {n, 1, z}] (* A203689 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203690 *)

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 04 2012