On Some Finite Sums with Factorials

Abstract

The summation formula $$\sum _{i=0}^{n-1}{\epsilon }^{i}i!(i^k+u_k)=v_k+{\epsilon }^{n-1}n!A_{k-1}(n)$$ $(ε=\pm 1; k=1,2,...; u_k, v_k\in \msbm\hbox{Z}; A_{k-1}$ is a polynomial) is derived and its various aspects are considered. In particular, divisibility with respect to $n$ is investigated. Infinitely many equivalents to Kurepa's hypothesis on the left factorial are found.

10 pages

References in corpus (1)

• On Some p-Adic Series with Factorials