$(x + x + \cdots + x)$, where $x$ added $n$ times can be written as $x * n$.
$(x * x * \cdots * x)$, where $x$ multiplied $n$ times can be written as $x ^ n$.
Is there an operator, such that if $x^{x^{\cdot^{\cdot^{x}}}}$, i.e. $x$ raised to the $x$th power $n$ times (with right associativity), we can write something like $x$ ¤ $n$, where the generic currency sign ¤ is a placeholder for the correct operator, if it exists?
Does such an operator exist? If so, what is the correct symbol? If not, why?
Is there a name for this operation? If so, what is it?