  Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a
field $K$ and let $M_{n,t}=(x^{e_1},\ldots, x^{e_n})$ be a monomial ideal of
$R$, where $x^{e_i}=x_1^t\ldots x_{i-1}^tx_{i+1}^t\ldots x_n^t$. We study the
unmixedness of its integral closure. Furthermore, we compute the Hilbert series
of this ideal and we show that this ideal is Freiman.
