A203689 Vandermonde sequence using x^2 + y^2 applied to (1,2,6,...,n!).

1, 5, 7400, 1515608208000, 67968144879431450715389952000, 2618461740951506934762583974466059060153960058218086400000

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 *)

Formula

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