Reversion of series---computing a series for the functional inverse of a function---has been in Maple since forever, but many people are not aware of how easy it is. Here's an example, where we are looking for "self-reverting" series---which I called "ambiverts". Anyway have fun.
PS There looks to be some "code rot" in the branch point series for Lambert W in Maple, which we encounter in that worksheet. Or, I may simply have not coded it very well in the first place (yeah, that was mine, once upon a time). Checking now. But there is a workaround (albeit an ugly one) shown in that worksheet.