with Raymond Kan, 2017, Journal of Computational and Graphical Statistics 26, 930-934. [Paper] [Internet Appendix] [Published Version] [Errata] [Code]. Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated multivariate normal distributions. Besides being numerically efficient, the proposed recursions also allow us to obtain explicit expressions of low order moments of folded and truncated multivariate normal distributions.