Tetration related to iterated exponentiation

Tetration related to iterated exponentiation

$^{2}n=n^{n}$

$^{3}n={(^{2}n)}^{(n^{n-1})}$

$^{4}n={(^{3}n)}^{(n^{(^{2}n-n}))}$

$^{5}n={(^{4}n)}^{(n^{(^{3}n-^{2}n}))}$

$^{6}n={(^{5}n)}^{(n^{(^{4}n-^{3}n}))}$

$^{k}n={(^{(k-1)}n)}^{(n^{(^{(k-2)}n-^{(k-3)}n}))}$ Only for K > 3

With enough nesting you can express tetration with only n and exponentiation by replacing the corresponding equalities. For example: $^{4}n={({(n^{n})}^{(n^{n-1})})}^{(n^{(n^{n}-n)})}$

Can this be noteworthy enough to be added in the tetration page?