[seqfan] Permutations Of +- Integers

[Leroy Quet]

This question is inspired by the game at:
http://gamesconceived.blogspot.com/2009/04/permutations-of-integers.html


Take the permutation, R= (r(1),r(2),r(3),...,r(n)), of (1,2,3,...,n). Then give a sign (+ or -) to each integer of the permutation to get (q(1),q(2),q(3),...q(n)). (In other words, each q(m) = + or - r(m).)
Let
Q(m) = sum{k=1 to m} q(k), for each m where 0 <= m <= n.
(Q(0) = 0.)

How many permutations R are such that, no matter how the signs are assigned to the integers of the permutation, then no |Q(m)| equals any |Q(j)|, for each j and m where 0 <= j < m <= n?

Is the sequence of the number of such permutations of (1,2,3,..,n) easily derived, or even trivially derived?

Thanks,
Leroy Quet