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a(n) = Product_{k=0..n} (n^6 + k^6).
6

%I #12 Dec 04 2023 04:18:40

%S 0,2,532480,615291760980,2759348178649088000,

%T 38607000141072009765625000,1421393314362014000255258433945600,

%U 120987688662917113214734283836109985530000,21538956798613753302336535534471908360548515840000,7407676630843157974199152503244776880017496531101658740000

%N a(n) = Product_{k=0..n} (n^6 + k^6).

%F a(n) ~ 2^(n + 1/2) * (2 + sqrt(3))^(sqrt(3)*n) * n^(6*n + 6) / exp((6 - Pi)*n).

%t Table[Product[n^6 + k^6, {k, 0, n}], {n, 0, 10}]

%o (PARI) a(n) = prod(k=0, n, n^6 + k^6); \\ _Michel Marcus_, Dec 02 2023

%Y Cf. A126804, A272244, A272246, A272247, A272248, A324439, A367833.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Dec 02 2023