A324425 a(n) = Product_{i=1..n, j=1..n, k=1..n} (i^2 + j^2 + k^2).

1, 3, 5668704, 550388591715704109656479285248, 152455602303300418998634460043817052571893573096619261814850281699755319515987050496

Offset: 0

Author

Vaclav Kotesovec, Feb 27 2019

Keywords

• nonn

Comments

(a(n)^(1/n^3))/n^2 tends to 0.828859579669279... = A306617.

Crossrefs

Cf. A079478, A306594, A368722, A368723.

Cf. A324403, A306617, A368622, A368623.

Programs

Maple

a:= n-> mul(mul(mul(i^2+j^2+k^2, i=1..n), j=1..n), k=1..n):
seq(a(n), n=0..5);  # Alois P. Heinz, Jun 24 2023

Mathematica

Table[Product[i^2+j^2+k^2, {i, 1, n}, {j, 1, n}, {k, 1, n}], {n, 1, 6}]
Clear[a]; a[n_] := a[n] = If[n == 1, 3, a[n-1] * Product[k^2 + j^2 + n^2, {j, 1, n}, {k, 1, n}]^3 * (3*n^2) / (Product[k^2 + 2*n^2, {k, 1, n}]^3)]; Table[a[n], {n, 1, 6}] (* Vaclav Kotesovec, Mar 27 2019 *)

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 24 2023