Inverse binomial transform of A114491.
This sequence enumerates a certain type of matroid, except for the first entry (which is 2 instead of 1). If the first entry is changed from 2 to 1, giving A118085, this enumerates "combinatorial geometries" on n labeled points.
These are matroids in which no element has rank 0; equivalently, all one-element sets are independent; equivalently, the closure of the empty set is empty.
These are called "simple matroids" in A002773. So A118085 is the "labeled" equivalent of that sequence, which counts unlabeled points.