Pentation

Pentation or quintation refers to the function $$a \uparrow\uparrow\uparrow b$$, where Arrow Notation is used. It produces numbers very much larger than those produced by tetration.

Pentation is less known than its tetrational cousin, but there are a few googologisms employing it: 3 pentated to 3 is known as the tritri, and 10 pentated to 100 is gaggol.

Sunir Shah uses the notation $$a * b$$ to indicate this function. Bowers calls it 'a to the b'th tower'. Sbiis Saibian uses the notation $$_{b \leftarrow}a$$.

Pseudocode
Below is an example of pseudocode for pentation.

function pentation(a, b): result := 1 repeat b times: result := a tetrated to result return result