Tetration Asymptotic Series

[Gottfried]

Code:

/*I've already initialized the base value as b=log(2)/2, and the beta polynomials, once you do that you can initialize the regular iteration, then you can run the code I'm writing*/

Also, do you know of any closed forms of the terms after the one where z is raised to the power of 2?

Since I see that "regular" and "Schroeder" has been mentioned, that evaluation of mine might match your query. (They show polynomials for the coefficients of the power serie)