  In $1961$, Mazur constructed a contractible, compact, smooth $4$-manifold
with boundary which is not homeomorphic to the standard $4$-ball, using a
$0$-handle, a $1$-handle and a $2$-handle. In this paper, for any integer
$n\geq2,$ we construct a contractible, compact, smooth $(n+3)$-manifold with
boundary which is not homeomorphic to the standard $(n+3)$-ball, using a
$0$-handle, an $n$-handle and an $(n+1)$-handle. The key step is the
construction of an interesting knotted $n$-sphere in $S^n\times S^2$
generalizing the Mazur pattern.
