

A135410


Number of permutations of {1,2,3,...,n} each with the same updown signature as its inverse permutation.


1



1, 1, 2, 4, 10, 26, 80, 272, 1076, 4848, 24832, 142340, 902440, 6257264, 47042924
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OFFSET

0,3


COMMENTS

An "updown signature" of the permutation (p(1),p(2),p(3),...,p(n)) is the sequence of (n1) signs (+ or ) where the kth 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 updown signature as their inverse permutations.
The terms were calculated by R. J. Mathar (see link).


LINKS

Table of n, a(n) for n=0..14.
R. J. Mathar, C== program


EXAMPLE

The updown 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 updown signature ++. So these two permutations, among others, are included in the count for n = 6.


CROSSREFS

Cf. A000085.
Sequence in context: A003239 A195924 A116673 * A148103 A148104 A179981
Adjacent sequences: A135407 A135408 A135409 * A135411 A135412 A135413


KEYWORD

nonn,more


AUTHOR

Leroy Quet, Dec 10 2007


EXTENSIONS

a(13)a(14) from Alois P. Heinz, Oct 18 2013


STATUS

approved



