A332344 a(n) is the number of permutations w of 1,2,...,n such that w is alternating and w^{-1} is reverse alternating.

1, 1, 0, 1, 1, 3, 6, 19, 56, 213, 816, 3717, 17408, 92935, 513152, 3147495, 19993728, 138638825, 995169664, 7700244745, 61608152704, 526317901451, 4642742078336, 43407723925499, 418444180284544, 4250149857500861, 44444888840063360

Offset: 0

Author

David Bevan, Feb 10 2020

Keywords

• nonn

Examples

			The only alternating permutation of 1,2,3,4 whose inverse is reverse alternating is 2413.
The three alternating permutations of 1,...,5 whose inverses are reverse alternating are 24153, 24351 and 45231.
		

Links

• R. P. Stanley, Alternating permutations and symmetric functions, arXiv:math/0603520 [math.CO], 2006.

Crossrefs

For odd n, a(n) = A007999(n).

For even n > 1, a(n) = A007999(n) - A007999(n-2).

For n > 1, a(n) = A332345(n)/2 - A007999(n).