OFFSET
0,2
COMMENTS
In general, for p>=1, Product_{k=0..n} (n^p + k^p) ~ sqrt(2) * n^(p*(n+1)) * exp(n*Sum_{j>=1} (-1)^(j+1) / (j*(1 + j*p))).
FORMULA
a(n) ~ 2^(2*n+1/2) * phi^(sqrt(5)*n) * n^(5*n+5) / exp((5-sqrt(phi)*Pi/5^(1/4))*n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
MATHEMATICA
Table[Product[n^5+k^5, {k, 0, n}], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Apr 23 2016
STATUS
approved