We provide a very short proof of a Qi-Zhao-Guo closed form for derangements numbers based on the determinants of certain Hessenberg matrices. The proof is grounded on a basic result on finite sequences and an inductive argument.

中文翻译：

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乱序数的封闭形式：基本证明

我们基于某些 Hessenberg 矩阵的行列式提供了一个非常简短的关于乱序数的 Qi-Zhao-Guo 封闭形式的证明。该证明基于有限序列的基本结果和归纳论证。