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

Parity alternating permutations starting with an odd integer