User blog comment:Alejandro Magno/Extended Arrow Notation/@comment-5150073-20140918210020/@comment-5150073-20140918230556

Not really, your ^'s work like powers of w:

^(^^(n)^^)^ = $$\omega^2$$

^(^^((n))^^)^ = $$\omega^2+1$$

^(^^(^(n)^)^^)^ = $$\omega^2+\omega$$

^(^^(^(^(n)^)^)^^)^ = $$\omega^2+\omega*2$$

^(^^(^^(n)^^)^^)^ = $$\omega^2*2$$

^(^^(^^(^^(n)^^)^^)^^)^ = $$\omega^2*3$$

^(^^^(n)^^^)^ = $$\omega^3$$

^(^^^((n))^^^)^ = $$\omega^3+1$$

^(^^^(^(n)^)^^^)^ = $$\omega^3+\omega$$

^(^^^(^^(n)^^)^^^)^ = $$\omega^3+\omega^2$$

^(^^^(^^^(n)^^^)^^^)^ = $$\omega^3*2$$

^(^^^(^^^(^^^(n)^^^)^^^)^^^)^ = $$\omega^3*3$$

^(^^^^(n)^^^^)^ = $$\omega^4$$

^(^^^^^(n)^^^^^)^ = $$\omega^5$$