Define $F(n,i)=\prod_{j=1}^nj^{j^i}$.
$F(n,0)=n!$.
$F(n,1)$ is hyperfactorial.
Is there a term for $F(n,i)$. How fast do these grow? Is growth rate $\Theta(n^{n^{i+1}})$?
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Is there a name for the fast growing functions?
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