CO37 Generating Functions: Definitions & Examples

Ordinary Generating Functions for Combinatorics. Definition, Discussion, and a few Examples. 0:38 Overview, 3:39 Definition and notation for the ordinary generating function of a sequence, 4:38 Example: generating function for reciprocals of factorials, 6:47 Convergence issues: the Calculus lens vs the Combinatorial lens, 11:40 Example: generating fcn for 1, 1, 1, ... 13:60 Example: generating fcn for a finite sequence of ones, 16:05 Example: generating fcn for (a row of) binomial coefficients, 18:01 Finding new power series starting with the power series for 1/(1-x) and the generating function for the sequence of the squares of positive integers.

A series of lectures on introductory Combinatorics. This full course is based on my book
Shahriar Shahriari, An Invitation to Combinatorics, Cambridge University Press, 2022.
For an annotated list of available Combinatorics videos see

Shahriari is the William Polk Russell Professor of Mathematics at Pomona College, Claremont CA

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[anansipotpourri]

thank you very much for the explanation, finally some video to tell me what is this function for, and eveerything else, explaining the functioning of things it takes from other subjects such as Calculus

[jiahao]

Does this contain lectures on Catalan Numbers ?