cp's OEIS Frontend

Let T_n denote the free idempotent monoid on n generators and alpha: T_n -> P([n]) the function sending an element to the generators appearing in it. Then this sequence is computed as the number of triples (S,D,p), where S is a "replete" subsemigroup of T_n (i.e. a subsemigroup for which (xuy) and (xvy) in S implies (xuvy) is in S), D is a "sparse" subset of T_n (i.e., for s and t in D, alpha(s) a subset of alpha(t) implies s = t), S "dominates" D (i.e. for s in S and t in D, alpha(s) is not a subset of alpha(t) and S is closed under multiplication by elements of D) and p is a "parity" function from the image of S under alpha to {0,1}. See Rogers 2024.