Comtet, Louis Advanced combinatorics. The art of finite and infinite expansions. Translated from the French by J. W. Nienhuys. Rev. and enlarged ed. (English) Zbl 0283.05001 Dordrecht, Holland - Boston, U.S.A.: D. Reidel Publishing Company. X, 343 p. Dfl. 65.00 (1974). Cited in 23 ReviewsCited in 1651 Documents MSC: 05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics × Cite Format Result Cite Review PDF Digital Library of Mathematical Functions: §26.3(iii) Recurrence Relations ‣ §26.3 Lattice Paths: Binomial Coefficients ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.3(i) Definitions ‣ §26.3 Lattice Paths: Binomial Coefficients ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.3(iv) Identities ‣ §26.3 Lattice Paths: Binomial Coefficients ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.3(v) Limiting Form ‣ §26.3 Lattice Paths: Binomial Coefficients ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.4(iii) Recurrence Relation ‣ §26.4 Lattice Paths: Multinomial Coefficients and Set Partitions ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.4(ii) Generating Function ‣ §26.4 Lattice Paths: Multinomial Coefficients and Set Partitions ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.4(i) Definitions ‣ §26.4 Lattice Paths: Multinomial Coefficients and Set Partitions ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.5(iii) Recurrence Relations ‣ §26.5 Lattice Paths: Catalan Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.5(ii) Generating Function ‣ §26.5 Lattice Paths: Catalan Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.5(i) Definitions ‣ §26.5 Lattice Paths: Catalan Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.6(iii) Recurrence Relations ‣ §26.6 Other Lattice Path Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.6(ii) Generating Functions ‣ §26.6 Other Lattice Path Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.6(i) Definitions ‣ §26.6 Other Lattice Path Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.7(iii) Recurrence Relation ‣ §26.7 Set Partitions: Bell Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.7(ii) Generating Function ‣ §26.7 Set Partitions: Bell Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.7(i) Definitions ‣ §26.7 Set Partitions: Bell Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.8(ii) Generating Functions ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.8(i) Definitions ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.8(iv) Recurrence Relations ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis §26.8(v) Identities ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis Chapter 26 Combinatorial Analysis Online Encyclopedia of Integer Sequences: Triangle read by rows, the coefficients of the Bell polynomials. Array T(n,k) = n*(binomial(k, 2) + 1) + k*(binomial(n, 2) + 1) read by antidiagonals.