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A159738 Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

%I A159738 #14 May 16 2022 02:44:01
%S A159738 14,168,1792,17920,172032,1605632,14680064,132120576,1174405120,
%T A159738 10334765056,90194313216,781684047872,6734508720128,57724360458240,
%U A159738 492581209243648,4186940278571008,35465847065542656,299489375220137984
%N A159738 Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
%H A159738 R. H. Hardin, <a href="/A159738/b159738.txt">Table of n, a(n) for n=2..100</a>
%H A159738 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-64).
%F A159738 a(n) = (copies*n)*(copies+1)^(n-2).
%F A159738 From _G. C. Greubel_, Jun 01 2018: (Start)
%F A159738 a(n) = 7*n*8^(n-2).
%F A159738 a(n) = 16*a(n-1) - 64*a(n-2).
%F A159738 G.f.: x^2*(14-56*x)/(1-16*x+64*x^2).
%F A159738 E.g.f.: 7*x*exp(8*x)/8. (End)
%F A159738 From _Amiram Eldar_, May 16 2022: (Start)
%F A159738 Sum_{n>=2} 1/a(n) = (64/7)*log(8/7) - 8/7.
%F A159738 Sum_{n>=2} (-1)^n/a(n) = 8/7 - (64/7)*log(9/8). (End)
%t A159738 LinearRecurrence[{16,-64}, {14,168}, 30] (* or *) Table[7*n*8^(n-2), {n,2,30}] (* _G. C. Greubel_, Jun 01 2018 *)
%o A159738 (PARI) for(n=2,30, print1(7*n*8^(n-2), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%o A159738 (Magma) I:=[14, 168]; [n le 2 select I[n] else 16*Self(n-1) - 64*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jun 01 2018
%Y A159738 Cf. A159715, A159721, A159727, A159733, A159736, A159739, A159740.
%K A159738 nonn
%O A159738 2,1
%A A159738 _R. H. Hardin_, Apr 20 2009