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%I #11 Jul 17 2020 13:03:33
%S 0,150,2763,28236,251205,2116386,17292639,138352920,1089544473,
%T 8474253870,65251778163,498286334052,3778671399789,28485369052602,
%U 213640267939335,1595180667331632,11864156213337153,87934334287152582,649737025566256155,4787535977856705660
%N Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
%H Andrew Howroyd, <a href="/A151607/b151607.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (17,-94,190,-161,49).
%F a(n) = n*(3*7^n - 36*n) for n > 1. - _Andrew Howroyd_, May 04 2020
%F From _Colin Barker_, Jul 17 2020: (Start)
%F G.f.: 3*x^2*(50 + 71*x - 1545*x^2 + 805*x^3 - 245*x^4) / ((1 - x)^3*(1 - 7*x)^2).
%F a(n) = 17*a(n-1) - 94*a(n-2) + 190*a(n-3) - 161*a(n-4) + 49*a(n-5) for n>6.
%F (End)
%o (PARI) a(n) = if(n <= 1, 0, n*(3*7^n - 36*n)) \\ _Andrew Howroyd_, May 04 2020
%o (PARI) concat(0, Vec(3*x^2*(50 + 71*x - 1545*x^2 + 805*x^3 - 245*x^4) / ((1 - x)^3*(1 - 7*x)^2) + O(x^40))) \\ _Colin Barker_, Jul 17 2020
%Y Cf. A151583.
%K nonn,easy
%O 1,2
%A _R. H. Hardin_, May 21 2009
%E Terms a(7) and beyond from _Andrew Howroyd_, May 04 2020
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