Combinatorics
Combinatorics. Instructor: Prof. Sunil Chandran, Department of Computer Science and Automation, IISc Bangalore. This course covers the topics typically covered in a first level combinatorics course. It introduces the elementary notions in combinatorics and presents the most elementary techniques in combinatorics - pigeonhole principle, inclusion-exclusion principle, recurrence relations and generating functions.
(from nptel.ac.in )

Lecture 36 - Partition Number Part 4, Catalan Numbers Part 1
VIDEO

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Pigeonhole Principle
Lecture 01 - Pigeon Hole Principle, Part 1
Lecture 02 - Pigeonhole Principle, Part 2
Lecture 03 - Pigeonhole Principle, Part 3
Lecture 04 - Pigeonhole Principle, Part 4
Elementary Concepts
Lecture 05 - Elementary Concepts and Basic Counting Principles
Lecture 06 - Elementary Concepts; Binomial Theorem; Bijective Proofs Part 1
Lecture 07 - Bijective Proofs Part 2
Lecture 08 - Bijective Proofs Part 3; Properties of Binomial Coefficients; Combinatorial Identities
Lecture 09 - Combinatorial Identities Part 2; Permutations of Multisets Part 1
Lecture 10 - Permutations of Multisets Part 2
Lecture 11 - Multinomial Theorem, Combinations of Multisets Part 1
Lecture 12 - Combinations of Multisets Part 2
Lecture 13 - Combinations of Multisets Part 3, Bounds for Binomial Coefficients
Lecture 14 - Stirling's Formula, Generalization of Binomial Coefficients Part 1
Lecture 15 - Generalization of Binomial Coefficients Part 2
Lecture 16 - Generalization of Binomial Coefficients Part 3, Double Counting Part 1
Some Techniques
Lecture 17 - Double Counting Part 1
Lecture 18 - Hall's Theorem for Regular Bipartite Graphs; Inclusion-Exclusion Principle Part 1
Lecture 19 - Inclusion-Exclusion Principle Part 2
Lecture 20 - Inclusion-Exclusion Principle Part 3
Lecture 21 - Inclusion-Exclusion Principle Part 4
Lecture 22 - Inclusion-Exclusion Principle Part 5
Recurrence Relations and Generating Functions
Lecture 23 - Recurrence Relations Part 1
Lecture 24 - Recurrence Relations Part 2
Lecture 25 - Recurrence Relations Part 3
Lecture 26 - Recurrence Relations Part 4
Lecture 27 - Recurrence Relations Part 5
Lecture 28 - Generating Functions Part 1
Lecture 29 - Generating Functions Part 2
Lecture 30 - Solving Recurrence Relations using Generating Functions Part 1
Lecture 31 - Solving Recurrence Relations using Generating Functions Part 2
Lecture 32 - Exponential Generating Functions Part 1
Lecture 33 - Exponential Generating Functions Part 2, Partition Number Part 1
Special Numbers
Lecture 34 - Partition Number Part 2
Lecture 35 - Partition Number Part 3
Lecture 36 - Partition Number Part 4, Catalan Numbers Part 1
Lecture 37 - Catalan Numbers Part 2
Lecture 38 - Catalan Numbers Part 3, Stirling Numbers of the Second Kind
Lecture 39 - Difference Sequences
Lecture 40 - Stirling Numbers
Lecture 41 - Summary