  A Parity Alternating Permutation of the set $[n] = \{1, 2,\ldots, n\}$ is a
permutation with even and odd entries alternatively. We deal with parity
alternating permutations having an odd entry in the first position, PAPs. We
study the numbers that count the PAPs with even as well as odd parity. We also
study a subclass of PAPs being derangements as well, Parity Alternating
Derangements (PADs). Moreover, by considering the parity of these PADs we look
into their statistical property of excedance.
