cp's OEIS Frontend

A159740 Number of permutations of 9 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

%I A159740 #13 May 16 2022 02:43:26
%S A159740 18,270,3600,45000,540000,6300000,72000000,810000000,9000000000,
%T A159740 99000000000,1080000000000,11700000000000,126000000000000,
%U A159740 1350000000000000,14400000000000000,153000000000000000
%N A159740 Number of permutations of 9 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
%H A159740 R. H. Hardin, <a href="/A159740/b159740.txt">Table of n, a(n) for n=2..100</a>
%H A159740 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).
%F A159740 a(n) = (copies*n)*(copies+1)^(n-2).
%F A159740 From _G. C. Greubel_, Jun 01 2018: (Start)
%F A159740 a(n) = 9*n*10^(n-2).
%F A159740 G.f.: x^2*(18-90*x)/(1-20*x+100*x^2).
%F A159740 E.g.f.: 9*x*exp(10*x)/10. (End)
%F A159740 From _Amiram Eldar_, May 16 2022: (Start)
%F A159740 Sum_{n>=2} 1/a(n) = (100/9)*log(10/9) - 10/9.
%F A159740 Sum_{n>=2} (-1)^n/a(n) = 10/9 - (100/9)*log(11/10). (End)
%t A159740 LinearRecurrence[{20,-100}, {18,270}, 30] (* or *) Table[9*n*10^(n-2), {n,2,30}] (* _G. C. Greubel_, Jun 01 2018 *)
%o A159740 (PARI) m=30; v=concat([18, 270], vector(m-2)); for(n=3, m, v[n]=20*v[n-1] -100*v[n-2]); v \\ _G. C. Greubel_, Jun 01 2018
%o A159740 (Magma) I:=[18, 270]; [n le 2 select I[n] else 20*Self(n-1) - 100*Self(n-2): n in [1..10]]; // _G. C. Greubel_, Jun 01 2018
%Y A159740 Cf. A159715, A159721, A159727, A159733, A159736, A159738, A159739.
%K A159740 nonn
%O A159740 2,1
%A A159740 _R. H. Hardin_, Apr 20 2009