  In this note, by using the Hasse-Teichm\"uller derivatives, we obtain two
explicit expressions for the related numbers of higher order Appell
polynomials. One of them presents a determinant expression for the related
numbers of higher order Appell polynomials, which involves several determinant
expressions of special numbers, such as the higher order generalized
hypergeometric Bernoulli and Cauchy numbers, thus recovers the classical
determinant expressions of Bernoulli and Cauchy numbers stated in an article by
Glaisher in 1875.

Number Theory