Let \begin{equation*}%\label{Fall-Factorial-Dfn-Eq} \langle\alpha\rangle_n= \prod_{k=0}^{n-1}(\alpha-k)= \begin{cases} \alpha(\alpha-1)\dotsm(\alpha-n+1), & n\ge1\\ 1,& n=0 \end{cases} \end{equation*} and \begin{equation*} (\alpha)_n=\prod_{\ell=0}^{n-1}(\alpha+\ell) = \begin{cases} \alpha(\alpha+1)\dotsm(\alpha+n-1), & n\ge1\\ 1, & n=0 \end{cases} \end{equation*} denote the falling and rising factorials of $\alpha\in\mathbb{C}$ respectively. In Remark 3.1 of the paper [1] below, the formula \begin{equation}\label{Bell-1-lambda}\tag{1} B_{n,k}\Biggl(1, 1-\alpha, (1-\alpha)(1-2\alpha),\dotsc, \prod_{\ell=0}^{n-k}(1-\ell\alpha)\Biggr) =\frac{(-1)^k}{k!} \sum_{\ell=0}^k (-1)^{\ell} \binom{k}{\ell} \prod_{q=0}^{n-1}(\ell-q\alpha) \end{equation} for $\alpha\in\mathbb{C}$ and $n\ge k\ge0$ was concluded. In Theorem 2.1 of the paper [2] below, the formulas \begin{equation}\label{Bell-fall-Eq}\tag{2} B_{n,k}(\langle\alpha\rangle_1, \langle\alpha\rangle_2, \dotsc,\langle\alpha\rangle_{n-k+1}) =\frac{(-1)^k}{k!}\sum_{\ell=0}^{k}(-1)^{\ell}\binom{k}{\ell}\langle\alpha\ell\rangle_n \end{equation} and \begin{equation}\label{Bell-fall-Eq-inv}\tag{3} \sum_{\ell=0}^{k}\frac{B_{n,\ell}(\langle\alpha\rangle_1, \langle\alpha\rangle_2, \dotsc,\langle\alpha\rangle_{n-\ell+1})}{(k-\ell)!} =\frac{\langle\alpha k\rangle_n}{k!} \end{equation} for $n\ge k\ge0$ and $\alpha\in\mathbb{R}$ were established. As consequences of the formulas \eqref{Bell-fall-Eq} and \eqref{Bell-fall-Eq-inv}, the formulas \begin{equation}\label{Bell-rise-Eq}\tag{4} B_{n,k}((\alpha)_1, (\alpha)_2, \dotsc, (\alpha)_{n-k+1}) =\frac{(-1)^k}{k!}\sum_{\ell=0}^{k}(-1)^{\ell}\binom{k}{\ell}(\alpha\ell)_n \end{equation} and \begin{equation}\label{Bell-rise-Eq-inv}\tag{5} \sum_{\ell=0}^{k}\frac{B_{n,\ell}((\alpha)_1, (\alpha)_2, \dotsc, (\alpha)_{n-\ell+1})}{(k-\ell)!} =\frac{(\alpha k)_n}{k!} \end{equation} for $\alpha\in\mathbb{C}$ and $n\ge k\ge0$ were derived in Corollary 2.1 of the paper [2]. The formulas \eqref{Bell-1-lambda} and \eqref{Bell-fall-Eq} were reviewed in Section 1.3 of the article [3] below. The formulas \eqref{Bell-1-lambda}, \eqref{Bell-fall-Eq}, and \eqref{Bell-rise-Eq} are equivalent to \begin{equation}\tag{6} B_{n,k}(\langle\alpha\rangle_1, \langle\alpha\rangle_2, \dotsc,\langle\alpha\rangle_{n-k+1}) =\sum _{j=k}^n s(n,j)\alpha^jS(j,k) \end{equation} for $n\ge k\ge0$ and $\alpha\in\mathbb{R}$ at https://mathoverflow.net/a/88071/147732, where $s(n,j)$ and $S(j,k)$ stand for the Stirling numbers of the first and second kinds respectively. References 1. B.-N. Guo and F. Qi, *Viewing some ordinary differential equations from the angle of derivative polynomials*, Iran. J. Math. Sci. Inform. **16** (2021), no. 1, 77--95; available online at https://doi.org/10.29252/ijmsi.16.1.77. 2. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, *Closed formulas and identities for the Bell polynomials and falling factorials*, Contributions to Discrete Mathematics **15** (2020), no. 1, 163--174; available online at https://doi.org/10.11575/cdm.v15i1.68111. 3. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Yong-Hong Yao, *Special values of the Bell polynomials of the second kind for some sequences and functions*, Journal of Mathematical Analysis and Applications **491** (2020), no. 2, Paper No.124382, 31 pages; available online at https://doi.org/10.1016/j.jmaa.2020.124382.