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%I #7 May 05 2020 19:25:45
%S 0,5,156,2114,19328,140571,882340,5007112,26441856,132439905,
%T 637468300,2976161790,13569454592,60725449335,267757190100,
%U 1166662948900,5034645823680,21556696454685,91704869986620,388044105102650,1634678955350400,6860481786528275,28700914012807556
%N Number of permutations of 1..n arranged in a circle with exactly 4 adjacent element pairs in decreasing order.
%H Andrew Howroyd, <a href="/A151577/b151577.txt">Table of n, a(n) for n = 4..500</a>
%F From _Andrew Howroyd_, May 05 2020: (Start)
%F a(n) = n*A000498(n-1).
%F a(n) = n*(4^(n-1) - n*3^(n-1) + binomial(n,2)*2^(n-1) - binomial(n,3)). (End)
%o (PARI) a(n) = {n*(4^(n-1) - n*3^(n-1) + binomial(n,2)*2^(n-1) - binomial(n,3))} \\ _Andrew Howroyd_, May 05 2020
%Y Column k=4 of A334218.
%Y Cf. A000498.
%K nonn
%O 4,2
%A _R. H. Hardin_, May 21 2009
%E Terms a(17) and beyond from _Andrew Howroyd_, May 05 2020
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