

A327091


Number of chiral pairs of length n words with integer entries that cover an initial interval of positive integers.


2



0, 1, 5, 36, 264, 2335, 23609, 272880, 3543360, 51123511, 811313945, 14045781456, 263429150544, 5320671461575, 115141595216009, 2657827340717760, 65185383511024320, 1692767331624879031, 46400793659613081785, 1338843898122140977776, 40562412499251225624624
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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

Row sums of A305622.
Sequence in context: A297576 A164110 A285392 * A201351 A253470 A188899
Adjacent sequences: A327088 A327089 A327090 * A327092 A327093 A327094


KEYWORD

nonn


AUTHOR

Andrew Howroyd, Sep 13 2019


STATUS

approved



