Combinatorics and Graph Theory

    

Stirling Numbers Via Combinatorial Sums

Authors: Anwesh Bhattacharya

In this paper, we have derived a formula to find combinatorial sums of the type $\sum_{r=0}^n r^k {n\choose r}$ for $k \in \mathbb{N}$. The formula is conveniently expressed as a linear combination of terms involving the falling factorial. The co-efficients in this linear expression satisfy a recurrence relation, which is identical to that of the Stirling numbers of the first and second kind.

Comments: 10 Pages. Presented at MMLA 2019, PES University, Bangalore.

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Submission history

[v1] 2020-12-14 12:36:29
[v2] 2020-12-18 01:09:28

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