Secant Number

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)

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