User blog comment:Luckyluxius/KeyArrow Notation extension/@comment-44079442-20191204043418

a|1|b grows roughly double exponentially as b increases, and a|2|b is equal to a^((a^b^b)^(a^b^b)), which grows quadruple exponentially (the first few values of 2|2|n are 2^2^64, 2^(2^3623878656), 2^(2^(2^264)), and 2^2^(3125*2^3125)). In general, a|n|b grows at a rate comparable to a^a^...a^a^b w/ 2n copies of a. Now, a|1|b|c obviously grows tetrationally as c increases. The first few values of a|2|1|c for a = 2 are 2|1|1|(2|1|1|2) = 2|1|1|4 = 65536, 2|1|1|(2|1|1|3) = 2|1|1|16 = 2^^16, 2|1|1|(2|1|1|4) = 2|1|1|65536 = 2^^65,536 (which is the same as 2^^^4), meaning that a|d|b|c grows at roughly the same rate as a^^(a^^b) as c increases. Beyond that, I haven't analyzed the growth rate very much, but I assume a|b|c|d|e is equal to a|b-1|c|d|(a|b-1|c|d|e), based on the definition for 4 arguments.