On Some Finite Sums with Factorials
Branko Dragovich
Abstract
The summation formula Σn-1i=0εi i! (ik+uk) = vk+εn-1 n! Ak-1(n) (ε= 1; k=1,2,...; uk, vk∈ Z; Ak-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.
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