  Monotone triangles are certain triangular arrays of integers, which
correspond to $n \times n$ alternating sign matrices when prescribing
$(1,2,...,n)$ as bottom row of the monotone triangle. In this article we define
halved monotone triangles, a specialization of which correspond to vertically
symmetric alternating sign matrices. We derive an operator formula for the
number of halved monotone triangles with prescribed bottom row which is
analogous to our operator formula for the number of ordinary monotone triangle.
