Corrigendum to "Generators of the Hecke algebra of (S_(2n),B_n)"

In \cite{AC12}, among other things, we observed that the structure constants of the Hecke algebra of the Gel'fand pair $(S_{2n},B_n)$ are polynomials in $n$. It is brought to attention by Omar Tout that there is a missing argument in its proof. Here we provide the details of the missing argument by further analyzing various actions of the hyperoctahedral group.