I am looking for a description (if possible with proof) of a complete list of Casimir operators for the Jacobi Lie algebra, the semidirect product of the symplectic Lie algebra with a Heisenberg algebra.

I am looking for a complete description (if possible with proof) of the Casimir operators (i.e., generators and relations for the center of the universal enveloping algebra) for the Jacobi Lie algebra over the complex numbers, the semidirect product of the symplectic Lie algebra with a Heisenberg algebra.