Superfactorial

The superfactorial has two different versions. Pickover defines it as $$n\$ =\ ^2(n!) = \underbrace{n!^{n!^{n!^{.^{.^.}}}}}_{n!}$$, using $$n!$$ to represent the factorial. However, Simon and Plouffe define it as $$n\$ = \prod^{n}_{i = 1} i! = 1! \cdot 2! \cdot 3! \cdot 4! \cdot \ldots \cdot n! $$.