Geodesic
Some results on derangement polynomials
Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 3, pp. 307-313.

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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.
DOI : 10.14712/1213-7243.2022.025
Classification : 05A05, 05A16, 26A06
Keywords: derangement; permutation; integration 
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Hassani, Mehdi; Moshtagh, Hossein; Ghorbani, Mohammad. Some results on derangement polynomials. Commentationes Mathematicae Universitatis Carolinae, Tome 63 (2022) no. 3, pp. 307-313. doi : 10.14712/1213-7243.2022.025. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2022.025/

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