A convenient representation of the covariance matrix for a general $k$-level random, nested AOV model is obtained, as well as an expression for its inverse and determinant.
"Notes on the Covariance Matrix of a Random, Nested Anova Model." Ann. Math. Statist. 43 (2) 659 - 662, April, 1972. https://doi.org/10.1214/aoms/1177692648