 $$ \eqalign{   & Y(n,c) = \mathop {\int { \cdots \int {} } }\limits_{{\bf x}\, \in \,U(n,\,c)} \left( {\sum\limits_{0\, \le k\, \le \,n} {x_{\,k} ^0 } } \right)dx_{\,0}  \cdots dx_{\,n}  =   \cr    &  = \mathop {\int { \cdots \int {} } }\limits_{{\bf y}\, \in \,U(n,\,c)} \left( {\sum\limits_{0\, \le k\, \le \,n} {y_{\,k} ^0 } } \right)dy_{\,0}  \cdots dy_{\,n}  =   \cr    &  = \int_{t = 0