This might be a question people already asked or is obvious to experts, or is not appropriate for this forum, if so, I apologize. I am trying to calculate things like $z/(e^z1)$, or find the inverse of $x=z+ 2z+5z^2+\cdots$, expand as power series. What is the best (or favorite) software package you use to do stuff like this?

7$\begingroup$ Sage can do it: sagemath.org. (Search hint: finding the inverse function of a power series is called "Lagrange inversion", or sometimes "reversion".) $\endgroup$ – Tom Leinster Nov 3 '12 at 20:04

1$\begingroup$ Pari/GP's serreverse(). $\endgroup$ – Pasha Zusmanovich Nov 6 '12 at 16:47

1$\begingroup$ In flint library (flintlib.org) there's a bunch of functions for computing inverse series in different fields. For example, fmpz_poly_inv_series $\endgroup$ – Anton Apr 3 '13 at 2:16

1$\begingroup$ Assuming you mean the compositional inverse, fmpz_poly_revert_series. flint is a good choice if you want say 10000 terms. $\endgroup$ – Fredrik Johansson Apr 3 '13 at 22:57

2$\begingroup$ You don't say what kind of answer you're looking for. Would you be happy with a list of numerical values for a finite part of the list of coefficients or are you looking for something in a symbolic form where possible? $\endgroup$ – Dan Piponi May 25 '13 at 14:54
Okay, I've gathered the answers from the comments in alphabetical order.
flint has the fmpz_poly_revert_series command (A web search revealed a reference pdf, but no web page). Some benchmarks seem to indicate that flint is unusually fast.
Mathematica has the InverseSeries command.
Pari/GP has the serreverse function.
For the TInspire CAS calculator: http://www.ticalc.org/archives/files/fileinfo/424/42499.html.
Maple produces it. See http://www.maplesoft.com/support/help/Maple/view.aspx?path=powseries , especially the command http://www.maplesoft.com/support/help/Maple/view.aspx?path=powseries%2freversion for info.