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

0,6

Links

Table of n, a(n) for n=0..26.

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

Example

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.

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).

Sequence in context: A148572 A320174 A248603 * A345244 A052393 A024607

Adjacent sequences: A332341 A332342 A332343 * A332345 A332346 A332347

Keyword

nonn

Author

David Bevan, Feb 10 2020

Status

approved