The Hankel Determinant of Exponential Polynomials

The purpose of this note is two-fold. First we present evaluations of Hankel determinants of sequences of combinatorial interest related to partitions and permutations. Many such computations have been carried out by Radoux in his sequence of papers [2]–[5]. His proof methods include using a functional identity due to Sylvester and factoring the Hankel matrix. Second, unlike Radoux, we instead give bijective proofs to reveal the underlying structure of these identities.