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A159733 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

%I A159733 #22 May 16 2022 02:45:09
%S A159733 10,90,720,5400,38880,272160,1866240,12597120,83980800,554273280,
%T A159733 3627970560,23581808640,152374763520,979552051200,6269133127680,
%U A159733 39965723688960,253899891671040,1608032647249920,10155995666841600
%N A159733 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
%H A159733 R. H. Hardin, <a href="/A159733/b159733.txt">Table of n, a(n) for n = 2..100</a>
%H A159733 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-36).
%F A159733 a(n) = (copies*n)*(copies+1)^(n-2) where copies=5.
%F A159733 From _Colin Barker_, Mar 24 2018: (Start)
%F A159733 G.f.: 10*x^2*(1 - 3*x) / (1 - 6*x)^2.
%F A159733 a(n) = 12*a(n-1) - 36*a(n-2) for n>3. (End)
%F A159733 From _G. C. Greubel_, Jun 01 2018: (Start)
%F A159733 a(n) = 5*n*6^(n-2).
%F A159733 E.g.f.: 5*x*exp(6*x)/6. (End)
%F A159733 From _Amiram Eldar_, May 16 2022: (Start)
%F A159733 Sum_{n>=2} 1/a(n) = (36/5)*log(6/5) - 6/5.
%F A159733 Sum_{n>=2} (-1)^n/a(n) = 6/5 - (36/5)*log(7/6). (End)
%t A159733 LinearRecurrence[{12,-36}, {10,90}, 30] (* or *) Table[5*n*6^(n-2), {n,2,30}] (* _G. C. Greubel_, Jun 01 2018 *)
%o A159733 (PARI) for(n=2,30, print1(5*n*6^(n-2), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%o A159733 (Magma) [5*n*6^(n-2): n in [2..30]]; // _G. C. Greubel_, Jun 01 2018
%Y A159733 Cf. A159715, A159721, A159727, A159736, A159738, A159739, A159740.
%K A159733 nonn
%O A159733 2,1
%A A159733 _R. H. Hardin_, Apr 20 2009