Mehdi Hassani, Hossein Moshtagh, Mohammad Ghorbani
Some results on derangement polynomials

Comment.Math.Univ.Carolin. 63,3 (2022) 307-313.

Abstract: We study moments of the difference D_n(x)-x^n n! {\rm e}^{-1/x} concerning derangement polynomials D_n(x). For the first moment, we obtain an explicit formula in terms of the exponential integral function and we show that it is always negative for x>0. For the higher moments, we obtain a multiple integral representation of the order of the moment under computation.

Keywords: derangement; permutation; integration

DOI: DOI 10.14712/1213-7243.2022.025
AMS Subject Classification: 05A05 05A16 26A06