  The aim of this paper is to derive explicit formulas for two distinct values.
The first is the total number of symmetric peaks in a set partition of $[n]$
with exactly $k$ blocks, and the second one is the total number of
non-symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks. We
represent these results in two ways. First by using the theory of generating
functions, and the second by using combinatorial tools.
