  We derive a quadratic recursion relation for the linear Hodge integrals of
the form $\langle\tau_2^n\lambda_k\rangle$. These numbers are used in a formula
for Masur-Veech volumes of moduli spaces of quadratic differentials discovered
by Chen, M\"oller, and Sauvaget. Therefore, our recursion provides an efficient
way of computing these volumes.
