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%I #8 May 06 2020 01:37:41
%S 0,6,399,9528,140571,1561900,14413894,116857368,862140162,5925941490,
%T 38576132625,240659672336,1451515055333,8520359419080,48925419854400,
%U 275923203690000,1533178869210324,8414851432723230,45712442315346915,246193095207323400,1316311515774609375
%N Number of permutations of 1..n arranged in a circle with exactly 5 adjacent element pairs in decreasing order.
%H Andrew Howroyd, <a href="/A151578/b151578.txt">Table of n, a(n) for n = 5..500</a>
%F From _Andrew Howroyd_, May 05 2020: (Start)
%F a(n) = n*A000505(n-1).
%F a(n) = n*(5^(n-1) - n*4^(n-1) + binomial(n,2)*3^(n-1) - binomial(n,3)*2^(n-1) + binomial(n,4)). (End)
%o (PARI) a(n) = {n*(5^(n-1) - n*4^(n-1) + binomial(n,2)*3^(n-1) - binomial(n,3)*2^(n-1) + binomial(n,4))} \\ _Andrew Howroyd_, May 05 2020
%Y Column k=5 of A334218.
%Y Cf. A000505.
%K nonn
%O 5,2
%A _R. H. Hardin_, May 21 2009
%E Terms a(17) and beyond from _Andrew Howroyd_, May 05 2020
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