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%I #13 May 16 2022 02:44:17
%S 12,126,1176,10290,86436,705894,5647152,44471322,345888060,2663338062,
%T 20338217928,154231485954,1162668124884,8720010936630,65109414993504,
%U 484251274014186,3589156501516908,26519878594541598,195409631749253880
%N Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
%H R. H. Hardin, <a href="/A159736/b159736.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 (14,-49).
%F a(n) = (copies*n)*(copies+1)^(n-2).
%F From _G. C. Greubel_, Jun 01 2018: (Start)
%F a(n) = 6*n*7^(n-2).
%F a(n) = 14*a(n-1) - 49*a(n-2).
%F G.f.: x^2*(12-42*x)/(1-14*x+49*x^2).
%F E.g.f.: 6*x*exp(7*x)/7. (End)
%F From _Amiram Eldar_, May 16 2022: (Start)
%F Sum_{n>=2} 1/a(n) = (49/6)*log(7/6) - 7/6.
%F Sum_{n>=2} (-1)^n/a(n) = 7/6 - (49/6)*log(8/7). (End)
%t LinearRecurrence[{14,-49}, {12, 126}, 30] (* or *) Table[6*n*7^(n-2), {n, 2, 30}] (* _G. C. Greubel_, Jun 01 2018 *)
%o (PARI) for(n=2, 30, print1(6*n*7^(n-2), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%o (Magma) I:=[12, 126]; [n le 2 select I[n] else 14*Self(n-1) - 49*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jun 01 2018
%Y Cf. A159715, A159721, A159727, A159733, A159738, A159739, A159740.
%K nonn
%O 2,1
%A _R. H. Hardin_, Apr 20 2009
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