The subject is at the crossroads of Discrete Mathematics and Computer Science, with a strong probabilistic flavor. The main tools used before are on the one hand analytic (generating functions and complex analysis), and on the other probabilistic (strong laws, central limit theorems, martingales, etc.) Often, professionals worked with one set of tools or the other. We offer a reconciliation to espouse these fields to come in hand-in-hand offering a harmonious and beneficial marriage.