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A159739 Number of permutations of 8 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

%I A159739 #18 May 16 2022 02:43:44
%S A159739 16,216,2592,29160,314928,3306744,34012224,344373768,3443737680,
%T A159739 34093003032,334731302496,3263630199336,31632108085872,
%U A159739 305023899399480,2928229434235008,28001193964872264,266834907194665104,2534931618349318488,24015141647519859360
%N A159739 Number of permutations of 8 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
%H A159739 R. H. Hardin, <a href="/A159739/b159739.txt">Table of n, a(n) for n=2..100</a>
%H A159739 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).
%F A159739 a(n) = (copies*n)*(copies+1)^(n-2) with copies = 8.
%F A159739 a(n) = 8*n*9^(n-2).
%F A159739 From _Colin Barker_, Feb 26 2018: (Start)
%F A159739 G.f.: 8*x^2*(2 - 9*x) / (1 - 9*x)^2.
%F A159739 a(n) = 18*a(n-1) - 81*a(n-2) for n>3.
%F A159739 (End)
%F A159739 From _Amiram Eldar_, May 16 2022: (Start)
%F A159739 Sum_{n>=2} 1/a(n) = (81/8)*log(9/8) - 9/8.
%F A159739 Sum_{n>=2} (-1)^n/a(n) = 9/8 - (81/8)*log(10/9). (End)
%t A159739 LinearRecurrence[{18,-81}, {16,216}, 30] (* _G. C. Greubel_, Jun 01 2018 *)
%o A159739 (PARI) Vec(8*x^2*(2 - 9*x) / (1 - 9*x)^2 + O(x^25)) \\ _Colin Barker_, Feb 26 2018
%o A159739 (Magma) I:=[16, 216]; [n le 2 select I[n] else 18*Self(n-1) - 81*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jun 01 2018
%Y A159739 Cf. A159715, A159721, A159727, A159733, A159736, A159738, A159740.
%K A159739 nonn,easy
%O A159739 2,1
%A A159739 _R. H. Hardin_, Apr 20 2009