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A326963 Number of length n arrays with entries that cover an initial interval of positive integers counting chiral pairs as equivalent, i.e., the arrays are reversible.

%I A326963 #10 Sep 16 2019 00:58:43
%S A326963 1,1,2,8,39,277,2348,23684,272955,3543901,51124052,811318628,
%T A326963 14045786139,263429197837,5320671508868,115141595761844,
%U A326963 2657827341263595,65185383518111581,1692767331631966292,46400793659715329348,1338843898122243225339,40562412499252848257197
%N A326963 Number of length n arrays with entries that cover an initial interval of positive integers counting chiral pairs as equivalent, i.e., the arrays are reversible.
%H A326963 Andrew Howroyd, <a href="/A326963/b326963.txt">Table of n, a(n) for n = 0..200</a>
%F A326963 a(n) = Sum_{k=0..n} (k!/2) * (Stirling2(n, k) + Stirling2(ceiling(n/2), k)).
%e A326963 a(3) = 8 because there are the following arrays up to reversal:
%e A326963    111,
%e A326963    112, 121, 122, 212,
%e A326963    123, 132, 213.
%o A326963 (PARI) a(n) = {sum(k=0, n, k! * (stirling(n, k, 2) + stirling((n+1)\2, k, 2)) / 2)}
%Y A326963 Row sums of A305621.
%K A326963 nonn
%O A326963 0,3
%A A326963 _Andrew Howroyd_, Sep 13 2019