cp's OEIS Frontend

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.

A Boolean function is ultrasweet if it is sweet (see A114302) under all permutations of the variables.

Two students, Shaddin Dughmi and Ian Post, have identified these functions as precisely the monotone Boolean functions whose prime implicants are the bases of a matroid, together with the constant function 0. This explains why a(n) = A058673(n) + 1.