Obrenović, Željko Experimental evaluation of user performance in a pursuit tracking task with multimodal feedback. (English) Zbl 1150.11345 Yugosl. J. Oper. Res. 14, No. 1, 99-115 (2004). For each \(k\geq1\) there are integers \(u_k\), \(v_k\), such that \[ \sum_{i=0}^{n-1}\varepsilon^ii!(i^k+u_k)=v_k+\varepsilon^{n-1}n!A_{k-1}(n), \] where \(\varepsilon=\pm1\) and \(A_{k-1}\) is a polynomial of degree \(k-1\). New equivalents of the Kurepa hypothesis [Đ. Kurepa, Math. Balk. 1, 147–153 (1971; Zbl 0224.10009)] on the left factorial are found. Reviewer: Miodrag Mihaljević (Beograd) MSC: 11B65 Binomial coefficients; factorials; \(q\)-identities Keywords:factorial sums; left factorial; Kurepa hypothesis Citations:Zbl 0224.10009 PDFBibTeX XMLCite \textit{Ž. Obrenović}, Yugosl. J. Oper. Res. 14, No. 1, 99--115 (2004; Zbl 1150.11345) Full Text: DOI