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 A159733 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum. 9
 10, 90, 720, 5400, 38880, 272160, 1866240, 12597120, 83980800, 554273280, 3627970560, 23581808640, 152374763520, 979552051200, 6269133127680, 39965723688960, 253899891671040, 1608032647249920, 10155995666841600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS R. H. Hardin, Table of n, a(n) for n = 2..100 Index entries for linear recurrences with constant coefficients, signature (12,-36). FORMULA a(n) = (copies*n)*(copies+1)^(n-2) where copies=5. From Colin Barker, Mar 24 2018: (Start) G.f.: 10*x^2*(1 - 3*x) / (1 - 6*x)^2. a(n) = 12*a(n-1) - 36*a(n-2) for n>3. (End) From G. C. Greubel, Jun 01 2018: (Start) a(n) = 5*n*6^(n-2). E.g.f.: 5*x*exp(6*x)/6. (End) From Amiram Eldar, May 16 2022: (Start) Sum_{n>=2} 1/a(n) = (36/5)*log(6/5) - 6/5. Sum_{n>=2} (-1)^n/a(n) = 6/5 - (36/5)*log(7/6). (End) MATHEMATICA LinearRecurrence[{12, -36}, {10, 90}, 30] (* or *) Table[5*n*6^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *) PROG (PARI) for(n=2, 30, print1(5*n*6^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018 (Magma) [5*n*6^(n-2): n in [2..30]]; // G. C. Greubel, Jun 01 2018 CROSSREFS Cf. A159715, A159721, A159727, A159736, A159738, A159739, A159740. Sequence in context: A306957 A319893 A319874 * A265325 A038726 A009454 Adjacent sequences: A159730 A159731 A159732 * A159734 A159735 A159736 KEYWORD nonn AUTHOR R. H. Hardin, Apr 20 2009 STATUS approved

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Last modified June 15 03:12 EDT 2024. Contains 373402 sequences. (Running on oeis4.)