Taro's multivariable Ackermann function

The Taro's multivariable Ackermann function \(A(a,b, …, z)\) is a recursive function invented by a Japanese googologist Taro (2007) and described in Fish (2013) . It is similar to Ackermann function with 2 variables, and with more than 3 variables grows at similar rate with Array notation, despite its simple definition.