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

Author

Richard Stanley, Jan 23 2025

Keywords

• nonn
• more

Examples

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

Links

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

Programs

Sage

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

Extensions

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

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