User blog comment:Alejandro Magno/Extended Arrow Notation/@comment-5150073-20140918210020

a^(n)^b ~ $$f_\omega(n)$$

a^((n))^b ~ $$f_{\omega+1}(n)$$

a^(((n)))^b ~ $$f_{\omega+2}(n)$$

a^(^(n)^)^b ~ $$f_{\omega*2}(n)$$

a^(^((n))^)^b ~ $$f_{\omega*2+1}(n)$$

a^(^(((n)))^)^b ~ $$f_{\omega*2+2}(n)$$

a^(^(^(n)^)^)^b ~ $$f_{\omega*3}(n)$$