Definition:Superfactorial

Definition
Let $n \in \Z_{\ge 0}$ be a positive integer.

The superfactorial of $n$ is defined as:
 * $n\$ = \displaystyle \prod_{k \mathop = 1}^n k! = 1! \times 2! \times \cdots \times \left({n - 1}\right)! \times n!$

where $k!$ denotes the factorial of $n$.

Also defined as
Some sources, for example, define the superfactorial as:
 * $n\$ = \dfrac {n!^{n!^{·^{·^{.^{n!}}}}}} {n!}$

but this is idiosyncratic and non-standard.

It is also not clear how high the tower of exponents is supposed to go.

, in his of $1997$, also defines the superfactorial as:


 * $n \$ = \underbrace{n!^{n!^{·^{·^{.^{n!}}}}} }_n$

which is found in the section for $3!^{3!^{3!} }$.