  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.
