Suppose that (a) is a set of n integers a_1> a_2>...>a_n >0 and that the sumset, the set of pairwise sums a_i + a_j , (i<=j), are all different. In how many ways can the sumset be ordered?
For example when n=2 the only possibility is 2 a_1 > a_1 + a_2 > 2 a_2.
When n=3 there are two possibilities.
One of these two is: 2 a_1 > a_1 + a_2 > 2 a_2 > a_1 + a_3 > a_2 + a_3 > 2 a_3.
For n=4 there are 10 possibilities.
This is similar to the sequence A0003121 in the OEIS.
This question was suggested by Moshe Newman
