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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

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