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%I #16 Jan 06 2024 14:28:31
%S 1,3,5668704,550388591715704109656479285248,
%T 152455602303300418998634460043817052571893573096619261814850281699755319515987050496
%N a(n) = Product_{i=1..n, j=1..n, k=1..n} (i^2 + j^2 + k^2).
%C (a(n)^(1/n^3))/n^2 tends to 0.828859579669279... = A306617.
%p a:= n-> mul(mul(mul(i^2+j^2+k^2, i=1..n), j=1..n), k=1..n):
%p seq(a(n), n=0..5); # _Alois P. Heinz_, Jun 24 2023
%t Table[Product[i^2+j^2+k^2, {i, 1, n}, {j, 1, n}, {k, 1, n}], {n, 1, 6}]
%t 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 *)
%Y Cf. A079478, A306594, A368722, A368723.
%Y Cf. A324403, A306617, A368622, A368623.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Feb 27 2019
%E a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2023
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