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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 31 2024
STATUS
approved