%I
%S 1,3,16,124,1262,15898,238572,4152172
%N Number of intervals in the weak (Bruhat) order of the symmetric group S_n that are distributive lattices.
%C The intervals [u,v] in the weak order that are distributive lattices are characterized by Stembridge. They are the intervals such that u^{1}.v is fully commutative, i.e. avoids the pattern 321.
%D J.R. Stembridge, On the Fully Commutative Elements of Coxeter Groups, Journal of Algebraic Combinatorics, 5 (1996), 353385.
%e Example: for n=3 there are six 1element intervals, six 2element intervals, and four intervals that are 3element chains, for a total of 16.
%K nonn,more
%O 1,2
%A _Richard Stanley_, May 07 2011
