A367833 a(n) = Product_{k=0..n} (n^8 + k^8).

0, 2, 33685504, 3851231199376068, 2670340833224951538384896, 8442437541556000328575439453125000, 96982590530284083757788173242580213780447232, 3406021755102121469537208768079471859185253483110025744

Offset: 0

Author

Vaclav Kotesovec, Dec 02 2023

Keywords

• nonn

Crossrefs

Cf. A126804, A272244, A272246, A272247, A272248, A367823.

Cf. A367834.

Programs

Mathematica

Table[Product[n^8 + k^8, {k, 0, n}], {n, 0, 10}]

Formula

a(n) ~ 2^(n + 1/2) * ((2 + sqrt(2 + sqrt(2)))/(2 - sqrt(2 + sqrt(2))))^(sqrt(2 + sqrt(2))*n/2) * (sqrt(2) - 1 + sqrt(4 - 2*sqrt(2)))^(sqrt(2 - sqrt(2))*n) * exp((Pi/sqrt(2 - sqrt(2)) - 8)*n) * n^(8*(n + 1)).