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
See also
Alternating Permutation, Euler Number, Euler Zigzag Number, Secant, Tangent Number, Zig Number
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References
Sloane, N. J. A. Sequence A000364/M4019 in "The On-Line Encyclopedia of Integer Sequences."
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Secant Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SecantNumber.html