A159739 - OEIS

%I #18 May 16 2022 02:43:44

%S 16,216,2592,29160,314928,3306744,34012224,344373768,3443737680,

%T 34093003032,334731302496,3263630199336,31632108085872,

%U 305023899399480,2928229434235008,28001193964872264,266834907194665104,2534931618349318488,24015141647519859360

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

%H R. H. Hardin, <a href="/A159739/b159739.txt">Table of n, a(n) for n=2..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).

%F a(n) = (copies*n)*(copies+1)^(n-2) with copies = 8.

%F a(n) = 8*n*9^(n-2).

%F From _Colin Barker_, Feb 26 2018: (Start)

%F G.f.: 8*x^2*(2 - 9*x) / (1 - 9*x)^2.

%F a(n) = 18*a(n-1) - 81*a(n-2) for n>3.

%F (End)

%F From _Amiram Eldar_, May 16 2022: (Start)

%F Sum_{n>=2} 1/a(n) = (81/8)*log(9/8) - 9/8.

%F Sum_{n>=2} (-1)^n/a(n) = 9/8 - (81/8)*log(10/9). (End)

%t LinearRecurrence[{18,-81}, {16,216}, 30] (* _G. C. Greubel_, Jun 01 2018 *)

%o (PARI) Vec(8*x^2*(2 - 9*x) / (1 - 9*x)^2 + O(x^25)) \\ _Colin Barker_, Feb 26 2018

%o (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 Cf. A159715, A159721, A159727, A159733, A159736, A159738, A159740.

%K nonn,easy

%O 2,1

%A _R. H. Hardin_, Apr 20 2009