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A324425
a(n) = Product_{i=1..n, j=1..n, k=1..n} (i^2 + j^2 + k^2).
9
1, 3, 5668704, 550388591715704109656479285248, 152455602303300418998634460043817052571893573096619261814850281699755319515987050496
OFFSET
0,2
COMMENTS
(a(n)^(1/n^3))/n^2 tends to 0.828859579669279... = A306617.
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 *)
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 27 2019
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jun 24 2023
STATUS
approved