A transversal matroid is a matroid whose independent sets are the partial transversals of a family of subsets of [1..n], while a bitransversal matroid is a transversal matroid whose dual is transversal. The principal (or fundamental) transversal matroids enumerated by A049312 form an important subset of bitransversal matroids.
Jensen, P. M., Binary fundamental matroids. Algebraic methods in graph theory, Vol. I, II (Szeged, 1978), pp. 281-296, Colloq. Math. Soc. Janos Bolyai, 25, North-Holland, Amsterdam-New York, 1981