The secant numbers 
,
also called the zig numbers or the Euler
numbers 
numbers than can be defined either in terms of a generating
function given as the Maclaurin series of
or as the numbers of alternating
permutations on 
,
4, 6, ... symbols (where permutations that are the reverses of one another counted
as equivalent). The first few 
for 
, 2, ... are 1, 5, 61, 1385, ... (OEIS A000364).
For example, the reversal-nonequivalent alternating permutations on 
and 4 numbers are 
, and 
, 
, 
, 
, 
, respectively.
The secant numbers have the generating function
 |  |  |
(1)
|
 |  |  |
(2)
|
