  We classify generalized distance-squared mappings of $\mathbb{R}^{n+1}$ into
$\mathbb{R}^{2n+1}$ ($n\ge 1$) having generic central points. Moreover, we show
that there does not exist a universal bad set $\Sigma\subset
(\mathbb{R}^{n+1})^{2n+1}$ in the case of this dimension-pair.
