In an alternating permutation of numbers 1 to n, the numbers are arranged so that they alternately increase and decrease. For example, there are five alternating permutations of the numbers 1, 2, 3, and 4:
1 3 2 4
1 4 2 3
2 3 1 4
2 4 1 3
3 4 1 2
Write a function to count the alternating permutations for a set of n numbers.
Suggestion: You might also try Cody Problem 46034.
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