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This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica (r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Key Features * Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences * Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions * Includes many new exercises with complete solutions at the end of each chapter This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and __Mathematica__(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Key Features\* Provides **new applications** on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences\* Features an **Appendix** on using **MAPLE(r)** and **__Mathematica (r)__** to generate functions\* Includes many **new exercises with complete solutions** at the end of each chapter Introductory Ideas And Examples -- Series -- Cards, Decks, And Hands: The Exponential Formula -- Applications Of Generating Functions -- Analytic And Asymptotic Methods -- Appendix: Using Maple[tm Superscript] And Mathematica[tm Superscript]. Herbert S. Wilf. Includes Bibliographical References (p. 224-226) And Index. An introduction to the use of generating functions and series in combinatorial mathematics. This edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polynominoes and exact covering sequences. A generating function is a clothesline on which we hang up a sequence of numbers for display.