%I A019589
%S A019589 1,2,5,16,59,246,1105,5270,26231,135036,713898,3857113
%N A019589 Number of nondecreasing sequences which are differences of two permutations 
               of 1,2,...,n.
%C A019589 Comments from Olivier GERARD (olivier.gerard(AT)gmail.com), Sep 18 2007: 
               (Start) Number of classes of permutations arrays giving the same 
               partition by the following transformation (equivalent in this case 
               to X-rays but more general): on the matrix representation of a permutation 
               of order n, the sum (i.e. here number of ones) in the i-th antidiagonal 
               is the number of copies of i in the partition.
%C A019589 This gives an injection of permutations of n into partitions with parts 
               at most 2n-1. The first or the last antidiagonal can be omitted, 
               reducing the size of parts to 2n-2 without changing the number of 
               classes.
%C A019589 This sequence is called Lambda_{n,1} in Louck's paper and appears explicitely 
               in p758. Terms up to 10 were computed by Myron Stein (arXiv).
%C A019589 This is similar to the number of Schur functions studied by Di Francesco 
               and al. (A007747) related to the powers of the Vandermonde determinant. 
               Also number of classes of straight (monotonic) crossing bi-permutations. 
               (End)
%D A019589 Olivier Gerard and Karol Penson, Set partitions, multiset permutations 
               and bi-permutations, in preparation.
%D A019589 James D. Louck, Power of a determinant with two physical applications, 
               Internat. J. Math. & Math. Sci., Vol. 22, No 4(1999) p745-759 - S 
               0161-1712(99)22745-7
%H A019589 C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, <a href="http:/
               /arXiv.org/abs/math.CO/0506334">On the x-rays of permutations</a>
%H A019589 J.-P. Davalan, <a href="http://jeux-et-mathematiques.davalan.org/mots/
               suites/tomo/index.html">Permutations et tomographie - X-rays</a>.
%Y A019589 Sequence in context: A019448 A000753 A007878 this_sequence A087949 A028333 
               A007747
%Y A019589 Adjacent sequences: A019586 A019587 A019588 this_sequence A019590 A019591 
               A019592
%K A019589 nonn,nice
%O A019589 1,2
%A A019589 Alex Postnikov (apost(AT)math.mit.edu)
%E A019589 More terms from Olivier GERARD (olivier.gerard(AT)gmail.com), Sep 18 
               2007
%E A019589 Two more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 04 2007