1,3

Also 1/(2^n*n!) * number of regions of hyperplane arrangements with normals (0,1,-1)^n

Comment from David 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)

T. Fine and J. Gill, Comparative probability relations, Ann. Prob. 4 (1976) 667-673.

D. Maclagan, Boolean Term Orders and the Root System B_n, Order 15 (1999), 279-295.

D. Maclagan, [math/9809134] Boolean Term Orders and the Root System B_n

Cf. A005806.

Sequence in context: A050561 A135865 A160710 this_sequence A048137 A005806 A015184

Adjacent sequences: A009994 A009995 A009996 this_sequence A009998 A009999 A010000

nonn,hard,nice

N. J. A. Sloane (njas(AT)research.att.com).

a(6) and a(7) from Diane Maclagan and Michael Kleber (maclagan(AT)math.berkeley.edu, michael.kleber(AT)gmail.com)

Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 26 2008