Submitted:
11 October 2016
Posted:
11 October 2016
You are already at the latest version
Abstract
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.
Keywords:
derangement number
; closed form
; Hessenberg determinant
; tridiagonal determinant
; generating function
; recurrence relation
; derivative
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