Wilf, Herbert S. Generatingfunctionology. 2nd ed. (English) Zbl 0831.05001 Boston, MA: Academic Press. x, 228 p. (1994). From the preface: “This edition contains several new areas of application in Chapter 4, many new problems and solutions, a number of improvements in the presentation, and corrections.”For a review of the first edition see Zbl 0689.05001. Cited in 5 ReviewsCited in 166 Documents MathOverflow Questions: Asymptotic for restricted compositions into k parts MSC: 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics 05A15 Exact enumeration problems, generating functions Citations:Zbl 0689.05001 PDFBibTeX XMLCite \textit{H. S. Wilf}, Generatingfunctionology. 2nd ed. Boston, MA: Academic Press (1994; Zbl 0831.05001) Digital Library of Mathematical Functions: Example 3 ‣ §26.18 Counting Techniques ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.7(i) Definitions ‣ §26.7 Set Partitions: Bell Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis Online Encyclopedia of Integer Sequences: Bell or exponential numbers: number of ways to partition a set of n labeled elements. Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points. Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n]. Number of connected labeled graphs with n nodes. Number of clouds with n points; number of undirected 2-regular labeled graphs; or number of n X n symmetric matrices with (0,1) entries, trace 0 and all row sums 2. Number of square permutations of n elements. Pascal’s triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n. Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n. Irregular triangle of numbers read by rows: {binomial(n-k, k), n >= 0, 0 <= k <= floor(n/2)}; or, triangle of coefficients of (one version of) Fibonacci polynomials. Nearest integer to n!/(2*log(2)^(n+1)). Number of derangements of n where minimal cycle size is at least 3. Number of labeled graphs with 2-colored nodes where black nodes are only connected to white nodes and vice versa. Number of labeled bipartite graphs with n nodes. Number of derangements of n where minimal cycle size is at least 4. Number of permutations of n elements admitting a cube root. Number of permutations of n elements admitting a fourth root. Triangle read by rows: T(n,k) (0<=k<=n) is the number of labeled graphs having k blue nodes and n-k green ones and only nodes of different colors can be joined by an edge. Number of labeled graphs having n blue nodes and n green ones, where edges join only nodes of different colors. Number of permutations on n points admitting a fifth root. Number of permutations on n points admitting a sixth root. Number of permutations on n points admitting a seventh root. Number A(n,k) of permutations on [n] that are the k-th power of a permutation; square array A(n,k), n>=0, k>=0, read by antidiagonals. Number of permutations on [n] admitting an eighth root. Number of permutations on [n] admitting a ninth root. Number of permutations on [n] admitting a tenth root. Number of permutations on [n] that are the n-th power of a permutation. Number of permutations of {1,2,...,n} having equal numbers of 1-cycles and 2-cycles.