A144924 - OEIS

%I #4 Oct 01 2013 03:21:04

%S 1,2,4,13,36,126,428,1681,6820,29233,127865,592604,2829477,14118079,

%T 72122117,380843081,2056927326,11444517369,65234523659,380644223976,

%U 2272831229113,13857568536672,86164285623173,546196787212398

%N Number of partition-type permutations in S_n.

%C 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 R. P. Stanley, Enumerative Combinatorics, Wadsworth, Vol. 1, 1986, Vol. 2, 1999; see especially Chapter 1.

%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999 (Chapter 7)

%e For n=3, the 4 partition-type permutations are (1 2 3) (1 3 2) (2 3 1) (3 2 1).

%K hard,nice,nonn

%O 1,2

%A _Sara Billey_, Sep 25 2008