A note about combinatorial sequences and Incomplete Gamma function

TL;DR

This paper explores properties of a family of sequences related to factorials and subfactorials, highlighting their connections to the Gamma and incomplete Gamma functions, providing insights into their mathematical structure.

Contribution

It introduces new properties and relations of a sequence family with Gamma functions, expanding understanding of their mathematical interplay.

Findings

Identifies interesting properties of the sequence family.

Establishes relations between sequences and Gamma functions.

Provides potential applications in mathematical analysis.

Abstract

In this short note we present a set of interesting and useful properties of a one-parameter family of sequences including factorial and subfactorial, and their relations to the Gamma function and the incomplete Gamma function.