Lah numbers, Laguerre polynomials of order negative one, and the nth derivative of exp(1/x)

Abstract

In this note we point out interesting connections among Lah numbers, Laguerre polynomials of order negative one, and exponential polynomials. We also discuss several different expressions for the nth derivative of exp(1/x). A new representation of this derivative is given in terms of exponential polynomials.

Keywords

• lah
• numbers
• stirling numbers
• laguerre polynomials
• exponential polynomials
• higher derivatives
• binomial identities
• 11m06
• 33b15