OFFSET
1,3
COMMENTS
If the word is achiral, i.e., the same as its reverse, we ignore it. If different from its reverse, we count it and its reverse as a chiral pair.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
a(n) = Sum_{k=1..n} (k!/2) * (Stirling2(n, k) - Stirling2(ceiling(n/2), k)).
EXAMPLE
a(3) = 5 because there are the following chiral pairs of words:
112/211, 122/221,
123/321, 132/231, 213/312.
PROG
(PARI) a(n) = {sum(k=1, n, k! * (stirling(n, k, 2) - stirling((n+1)\2, k, 2)) / 2)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Sep 13 2019
STATUS
approved