Jacobi-Trudi type formula for character of irreducible representations of $\mathfrak{g}\mathfrak{l}(m\mathrm{\mid }1)$

We prove a determinantal type formula to compute the irreducible characters of the general Lie superalgebra $\mathfrak{g}\mathfrak{l}(m\mathrm{\mid }1)$ in terms of the characters of the symmetric powers of the fundamental representation and their duals. This formula was conjectured by J. van der Jeugt and E. Moens for the Lie superalgebra $\mathfrak{g}\mathfrak{l}(m\mathrm{\mid }n)$ and generalizes the well-known Jacobi-Trudi formula.