CO27 What are the Stirling Numbers of the First Kind?

#stirling_numbers of the First Kind count the number of #permutations of a set that can be written as a product of k disjoint cycles. Or less formally, the number of ways of seating n people at k identical round tables (where the actual seats are identical and the only thing that matters is who is sitting to the left of who). Stirling Numbers of the First Kind are defined, a #recurrence relation is proved, and a formula for {n brack n-2} is given. Subscribe ‪@Shahriari‬ for more undergraduate math videos.
#combinatorics

00:00 Introduction
00:18 Definition: Stirling Numbers of the First Kind
02:48 Examples
06:43 Recurrence Relation (with proof)
10:16 Table of Small Values
10:37 A formula for {n brack n-2}

Videos on Stirling Numbers:
CO24: Stirling Numbers of the Second Kind    • CO24 The Stirling Numbers of the Second Kind  
CO25: A formula for Bell Numbers    • CO25 A formula for Bell Numbers  
CO26: Formulas for Stirling Numbers of the Second Kind    • CO26 Formulas for Stirling Numbers of the ...  
CO27: Stirling Numbers of the First Kind    • CO27 What are the Stirling Numbers of the ...  
CO28: Stirling #s of 1st Kind & Falling Factorials    • CO28 Stirling #s of 1st Kind & Expansion o...  
CO29: Stirling #s of 1st Kind vs 2nd Kind    • CO29 Stirling Numbers of First Kind vs Sti...  

Part of 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.
DOI: https://doi.org/10.1017/9781108568708
For an annotated list of available videos see
https://pomona.box.com/s/by2ay2872avx...
YouTube Playlist:    • Combinatorics, An Invitation  

Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA
Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and six time winner of Pomona College's Wig teaching award.