At a lower level than Flajolet and Sedgewick, Chapter 5 of [generatingfunctionology][1] by Wilf is a good introduction to complex analytic methods. (Yes, my two answers look very similar. As usual in a big list question, I am posting separate answers so people can vote on them separately.)


  [1]: http://www.math.upenn.edu/~wilf/gfology2.pdf