OFFSET
0,3
COMMENTS
An "up-down signature" of the permutation (p(1),p(2),p(3),...,p(n)) is the sequence of (n-1) signs (+ or -) where the k-th sign in the sequence is the sign of (p(k+1)-p(k)). All permutations of {1,2,3,...,n} which are their own inverses obviously have the same up-down signature as their inverse permutations.
The terms were calculated by R. J. Mathar (see link).
LINKS
R. J. Mathar, C++ program
EXAMPLE
The up-down signature of the permutation (4,2,6,3,5,1) is -+-+-. This permutation's inverse permutation is (6,2,4,1,5,3). The inverse permutation also has the up-down signature -+-+-. So these two permutations, among others, are included in the count for n = 6.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Leroy Quet, Dec 10 2007
EXTENSIONS
a(13)-a(14) from Alois P. Heinz, Oct 18 2013
a(15)-a(18) from Martin Ehrenstein, Jul 30 2023
STATUS
approved