A375845 a(n) = Product_{k=0..n} (k^8 + n).

0, 2, 1548, 20400912, 2237404520000, 1316258829530177400, 3107531556500789042401392, 23981023412887138890925360910336, 519343443733819692494314622381817102336, 28055691989665530513724742545624840551562500000

Offset: 0

Author

Vaclav Kotesovec, Aug 31 2024

Keywords

• nonn

Comments

In general, for m > 2, Product_{k=0..n} (k^m + n) ~ n^(m*n + (m+1)/2) / exp(m*n - Pi * n^(1/m) / sin(Pi/m)).

Crossrefs

Cf. A334411.

Cf. A126804 (m=1), A375839 (m=2), A375840 (m=3), A375841 (m=4), A375842 (m=5), A375843 (m=6), A375844 (m=7).

Programs

Mathematica

Table[Product[k^8 + n, {k, 0, n}], {n, 0, 15}]

Formula

a(n) ~ n^(8*n + 9/2) / exp(8*n - Pi*sqrt(2*(2+sqrt(2)))*n^(1/8)).