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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 20 13:44 EST 2021. Contains 340302 sequences. (Running on oeis4.)