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Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants
: Received: 11 October 2016 / Approved: 11 October 2016 / Online: 11 October 2016 (10:53:07 CEST)
In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.
derangement number; closed form; Hessenberg determinant; tridiagonal determinant; generating function; recurrence relation; derivative
Computer Science and Mathematics, Algebra and Number Theory
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