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A375845
a(n) = Product_{k=0..n} (k^8 + n).
6
0, 2, 1548, 20400912, 2237404520000, 1316258829530177400, 3107531556500789042401392, 23981023412887138890925360910336, 519343443733819692494314622381817102336, 28055691989665530513724742545624840551562500000
OFFSET
0,2
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)).
FORMULA
a(n) ~ n^(8*n + 9/2) / exp(8*n - Pi*sqrt(2*(2+sqrt(2)))*n^(1/8)).
MATHEMATICA
Table[Product[k^8 + n, {k, 0, n}], {n, 0, 15}]
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).
Sequence in context: A179866 A296362 A282999 * A201242 A062585 A239505
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 31 2024
STATUS
approved