  In 2017, O. Deiser and C. Lasser obtained an explicit formula for the $n$-th
derivative of the inverse tangent function. We calculate this derivative by a
different method based on Fa\`a di Bruno's formula. Comparing the two results
leads to the following identity for binomial coefficients:
$$\sum_{i=m}^{[n/2]}\frac{(-1)^i}{4^i}\binom{i}{m}\binom{n-i}{i}=\frac{(-1)^m}{2^n}\binom{n+1}{2m+1},$$
where $n,m\in \mathbb{N}_0$ and $m\leq [n/2]$. As was pointed out to the author
by C. Krattenthaler, this formula is a special case of Gau\ss's formula for the
hypergeometric function $_2F_1$.
