| Preface to the English Edition | p. xi |
| Preface | p. xiii |
| Formal Power Series and Generating Functions. Operations with Formal Power Series. Elementary Generating Functions | p. 1 |
| The lucky tickets problem | p. 1 |
| First conclusions | p. 6 |
| Generating functions and operations with them | p. 7 |
| Elementary generating functions | p. 10 |
| Differentiating and integrating generating functions | p. 12 |
| The algebra and the topology of formal power series | p. 13 |
| Problems | p. 14 |
| Generating Functions for Well-known Sequences | p. 17 |
| Geometric series | p. 17 |
| The Fibonacci sequence | p. 18 |
| Recurrence relations and rational generating functions | p. 21 |
| The Hadamard product of generating functions | p. 23 |
| Catalan numbers | p. 25 |
| Problems | p. 30 |
| Unambiguous Formal Grammars. The Lagrange Theorem | p. 35 |
| The Dyck Language | p. 35 |
| Productions in the Dyck language | p. 36 |
| Unambiguous formal grammars | p. 38 |
| The Lagrange equation and the Lagrange theorem | p. 42 |
| Problems | p. 43 |
| Analytic Properties of Functions Represented as Power Series and the Asymptotics of their Coefficients | p. 47 |
| Exponential estimates for asymptotics | p. 47 |
| Asymptotics of hypergeometric sequences | p. 50 |
| Asymptotics of coefficients of functions related by the Lagrange equation | p. 54 |
| Asymptotics of coefficients of generating series and singularities on the boundary of the disc of convergence | p. 56 |
| Problems | p. 58 |
| Generating Functions of Several Variables | p. 59 |
| The Pascal triangle | p. 59 |
| Exponential generating functions | p. 61 |
| The Dyck triangle | p. 63 |
| The Bernoulli-Euler triangle and enumeration of snakes | p. 64 |
| Representing generating functions as continued fractions | p. 72 |
| The Euler numbers in the triangle with multiplicities | p. 78 |
| Congruences in integer sequences | p. 79 |
| How to solve ordinary differential equations in generating functions | p. 82 |
| Problems | p. 83 |
| Partitions and Decompositions | p. 87 |
| Partitions and decompositions | p. 87 |
| The Euler identity | p. 92 |
| Set partitions and continued fractions | p. 95 |
| Problems | p. 98 |
| Dirichlet Generating Functions and the Inclusion-Exclusion Principle | p. 101 |
| The inclusion-exclusion principle | p. 101 |
| Dirichlet generating functions and operations with them | p. 104 |
| Mobius inversion | p. 107 |
| Multiplicative sequences | p. 109 |
| Problems | p. 110 |
| Enumeration of Embedded Graphs | p. 113 |
| Enumeration of marked trees | p. 113 |
| Generating functions for non-marked, marked, ordered, and cyclically ordered objects | p. 119 |
| Enumeration of plane and binary trees | p. 120 |
| Graph embeddings into surfaces | p. 122 |
| On the number of gluings of a polygon | p. 132 |
| Proof of the Harer-Zagier theorem | p. 136 |
| Problems | p. 140 |
| Final and Bibliographical Remarks | p. 143 |
| Bibliography | p. 145 |
| Index | p. 147 |
| Table of Contents provided by Ingram. All Rights Reserved. |
