  Let H be a symplectic vector space, let V be a vector space, and consider the
nilpotent Lie algebra L_H(V) = H \otimes V + S^2(V) with bracket [(h_1 \otimes
v_1;a_1),(h_2 \otimes v_2;a_2)] = (0,<h_1,h_2> v_1 v_2) . In this paper, we
calculate the Lie algebra homology of L_H(V) as a polynomial functor of V. This
has applications to the analysis of the Leray-Serre spectral sequence of the
fibrations of moduli spaces of pointed curves M_{1,n}->M_{1,1} and
M_{g,n}->M_g.
