Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers

Abstract

In the paper, the authors find several identities, including a new recurrence relation for the Stirling numbers of the first kind, involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers.

Keywords

• identity
• cauchy number
• lah number
• stirling number
• falling factorial
• rising factorial
• faà di bruno formula
• 11b73
• 11b83