Fourier coefficients of Eisenstein series on $\mathrm{S}\mathrm{O}(3,n+1)$

We explicitly compute Fourier coefficients of Eisenstein series on the special orthogonal group $G=\mathrm{S}\mathrm{O}(3,n+1)$ over $\mathbb{Q}$ with $n\ge 2$ which splits everywhere at finite places. We show that it has a bounded denominator.