Reference for Cardinality of Parabolic Subgroup of Symplectic Group over Finite Fields

Question

I am looking for a source to reference that gives the cardinality of parabolic subgroups of the Symplectic group $Sp$ over a finite field $\mathbb F_q$. What I want is essentially exactly what is in these lecture notes, but I need a proper citable source for it. Particularly, something which proves the cardinalities of the Levi and unipotent radical subgroups and concludes with (for some isotropic subspace of $\mathbb F_q^n$) $$|P(S)| = |N|\cdot |GL(k,\mathbb F_q)|\cdot |Sp(n-k, \mathbb F_q)|$$ and thus get $$|P(S)| = q^{\frac{k(k+1)}{2}+2k(n-k)} \prod_{i=0}^{k-1} (q^k-q^i) q^{(n-k)^2} \prod_{j=1}^{n-k}(q^{2j}-1)$$ Where $n$ is the dimension of the space initially and $k$ is the dimension of the isotropic subspace that is being stabalized.