[seqfan] Nathaniel Johnston's "orderings of pairs" A237749.

[Neil Sloane]

Dear Seq Fans, Nathaniel Johnston has submitted
a very nice sequence, A237749, The number of possible orderings of the real
numbers xi*xj (i <= j), subject to the constraint that x1 > x2 > ... > xn >
0. Offset 0, initial values 1, 1, 1, 2, 10, 114, 2608,
(and needs more terms).

But I have a strong sense that I've seen it
- or more likely something very like it - before.

This is exactly the kind of question that my old
colleague Peter Fishburn might have looked at - or
that might have been discussed in the journal *Order*.

 But I've searched briefly in the OEIS
and I cannot find the version that I remember.
Does any sequence fan recognize this problem?

Maybe if one looks at the products of more than two terms??

Neil