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Vote Winner: n<m>3 = n^^^m

Pentation Numbers are Hyper-Operators Number part.

Multiplication Numbers: n(m)

Exponentation Numbers: n<m>

Tetration Numbers: n<<m>> = n<m>2

Pentation Numbers: n<<<m>>> = n<m>3

Hexation Numbers: n<<<<m>>>> = n<m>4

Heptation Numbers: n<<<<<m>>>>> = n<m>5

etc.

Pentation Numbers start with 10^10^10^10^10^10^10^10^10^10 and end with 10^^10^^10^^10^^10^^10^^10^^10^^10^^10.

Hexation Numbers start with 10^^10^^10^^10^^10^^10^^10^^10^^10^^10 and end with 10^^^^10.

Heptation Numbers start with 10^^^^10 and end with 10^^^^^10.

etc.

X<<X>> = 10^^10

X<<X<X>>> = 10^^10^10

X<<X<<X>>>> = 10^^10^^10

X<<X<<X<<X>>>>>> = 10^^10^^10^^10

n<<n<<n...n<<n>>...>>>> (m n's) = n<<<m>>>

X<<<n>>> = 10^^^n

X<<<X>>> = 10^^^10

X<<<<n>>>> = 10^^^^n

X<<<<X>>>> = 10^^^^10

X<<<<<n>>>>> = 10^^^^^n

X<<<<<X>>>>> = 10^^^^^10

etc.

n<<...<<m>>...>> (l <> brackets) = n<m>l

n<m>l = {n,m,l}

X<X>X = {10,10,10} = tridecal

Next is Expansion, Multiexpansion, Powerexpansion, etc. Numbers.

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