# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a159727 Showing 1-1 of 1 %I A159727 #22 Oct 21 2022 22:06:59 %S A159727 8,60,400,2500,15000,87500,500000,2812500,15625000,85937500,468750000, %T A159727 2539062500,13671875000,73242187500,390625000000,2075195312500, %U A159727 10986328125000,57983398437500,305175781250000,1602172851562500 %N A159727 Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum. %H A159727 R. H. Hardin, Table of n, a(n) for n = 2..100 %H A159727 Index entries for linear recurrences with constant coefficients, signature (10,-25). %F A159727 a(n) = (4*n)*(4+1)^(n-2). %F A159727 From _Colin Barker_, Mar 23 2018: (Start) %F A159727 G.f.: 4*x^2*(2 - 5*x) / (1 - 5*x)^2. %F A159727 a(n) = 10*a(n-1) - 25*a(n-2) for n>3. (End) %F A159727 E.g.f.: 4*x*exp(5*x)/5. - _G. C. Greubel_, Jun 01 2018 %F A159727 From _Amiram Eldar_, May 16 2022: (Start) %F A159727 Sum_{n>=2} 1/a(n) = (25/4)*log(5/4) - 5/4. %F A159727 Sum_{n>=2} (-1)^n/a(n) = 5/4 - (25/4)*log(6/5). (End) %t A159727 LinearRecurrence[{10,-25}, {8,60}, 30] (* or *) Table[4*n*5^(n-2), {n,2,30}] (* _G. C. Greubel_, Jun 01 2018 *) %o A159727 (PARI) for(n=2, 30, print1(4*n*5^(n-2) , ", ")) \\ _G. C. Greubel_, Jun 01 2018 %o A159727 (Magma) [ 4*n*5^(n-2) : n in [2..30]]; // _G. C. Greubel_, Jun 01 2018 %Y A159727 Cf. A159715, A159721, A159733, A159736, A159738, A159739, A159740. %K A159727 nonn,easy %O A159727 2,1 %A A159727 _R. H. Hardin_, Apr 20 2009 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE