
COMMENTS

Also 1/(2^n*n!) * number of regions of hyperplane arrangements with normals (0,1,1)^n.
From David W. Wilson, Aug 15 2008: (Start)
Also, number of possible orderings of the set of divisors of a product of n distinct primes.
Let p1 < p2 < ... < p_n be primes (say p1 = p, p2 = q, p3 = r, ...) Consider the set M of divisors of p1*p2*...*p_n. How many ways can M be ordered?
For n = 0, we have m = { 1 }, with 1 ordering.
For n = 1, we have M = { 1, p }. There is 1 possible ordering, 1 < p.
For n = 2, we have M = { 1, p, q, pq }. Remembering p < q, there is again 1 possible ordering, 1 < p < q < pq.
For n = 3, we have M = { 1, p, q, r, pq, pr, qr, pqr }. There are 2 possible orderings here:
1 < p < q < r < pq < pr < qr < pqr,
1 < p < q < pq < r < pr < qr < pqr. (End)


LINKS

Table of n, a(n) for n=1..7.
Antoine Deza, George Manoussakis, Shmuel Onn, Primitive Zonotopes, Discrete & Computational Geometry, 2017, p. 113. (See p. 5.)
T. Fine and J. Gill, The enumeration of comparative probability relations, Ann. Prob. 4 (1976) 667673.
D. Maclagan, Boolean Term Orders and the Root System B_n, arXiv:math/9809134 [math.CO], 19981999.
D. Maclagan, Boolean Term Orders and the Root System B_n, Order 15 (1999), 279295.
