A380394 a(n) = number of possible pairs of descent sets of a permutation of 1,2,...,n and its inverse.

1, 1, 2, 6, 22, 94, 426, 1938, 8724, 38724, 169438, 731390, 3119052, 13162228

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Richard Stanley, Descent sets and inverse descent sets of a permutation, MathOverflow, 2025.

Example

For n=3 there are the six pairs (empty,empty), (1,1), (1,2), (2,1), (2,2), (12,12).

Prog

(Sage) def a380394(n): return len({ (tuple(p.descents()), tuple(p.idescents())) for p in Permutations(n) }) # Max Alekseyev, Jan 24 2025

Crossrefs

Sequence in context: A374544 A374545 A150274 * A109317 A109153 A030453

Adjacent sequences: A380391 A380392 A380393 * A380395 A380396 A380397

Keyword

nonn,more

Author

Richard Stanley, Jan 23 2025

Extensions

a(0)=1 prepended by Alois P. Heinz, Jan 25 2025

a(11)-a(13) from Max Alekseyev, Jan 28 2025

Status

approved