%I A144924
%S A144924 1,2,4,13,36,126,428,1681,6820,29233,127865,592604,2829477,14118079,
%T A144924 72122117,380843081,2056927326,11444517369,65234523659,380644223976,
%U A144924 2272831229113,13857568536672,86164285623173,546196787212398
%N A144924 Number of partition-type permutations in S_n.
%C A144924 These permutations satisfy the condition that their descent set corresponds 
               with a composition which is weakly decreasing under the bijection 
               between subsets of {1,2,...,n-1} to strict compositions of n via 
               {d_1<d_2<...<d_k} maps to (d_1,d_2-d_1,...,d_k-d_k-1,n-d_k)
%D A144924 R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, Vol. 
               2, 1999; see especially Chapter 1.
%D A144924 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999 (Chapter 
               7)
%e A144924 For n=3, the 4 partition-type permutations are (1 2 3) (1 3 2) (2 3 1) 
               (3 2 1).
%Y A144924 Sequence in context: A148249 A148250 A148251 this_sequence A148252 A148253 
               A148254
%Y A144924 Adjacent sequences: A144921 A144922 A144923 this_sequence A144925 A144926 
               A144927
%K A144924 hard,nice,nonn
%O A144924 1,2
%A A144924 Sara Billey (billey(AT)math.washington.edu), Sep 25 2008