I got in touch with Bruno Savy, one of the authors of the algolib package, and there is a function in the package called "equivalence" that produces such partial fraction expansions from generating functions in the format above. The result given is 

@Carl Love Hi Carl, best you take a look at the zip file here which has the maple code I used and the PDF of the paper I was writing, which explains teh GF a bit better and the approximations I made. You specifically want from equation (7) on in the paper, though you can read it al of course - thanks, Luke