The zag numbers (also called the 'tangent numbers') are defined as the set of numbers Tn satisfying the equation:
\ / 2n-1 \
tan(x) = > T | x |
/ n| --------- |
----- \ (2n-1)! /
The zag numbers, together with the zig numbers, form the alternating permutation set (the 'zigs' are even and the 'zags' are odd). The distinction between the odd and even 'zigzag' numbers is mostly due to the definition of one's basis in secant while the other is based on tangent (but also from the property of the even ones to have 'Euler regularity').
Info gathered from http://mathworld.wolfram.com/TangentNumber.html.