A159733 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
10, 90, 720, 5400, 38880, 272160, 1866240, 12597120, 83980800, 554273280, 3627970560, 23581808640, 152374763520, 979552051200, 6269133127680, 39965723688960, 253899891671040, 1608032647249920, 10155995666841600
Offset: 2
Keywords
Links
- R. H. Hardin, Table of n, a(n) for n = 2..100
- Index entries for linear recurrences with constant coefficients, signature (12,-36).
Programs
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Magma
[5*n*6^(n-2): n in [2..30]]; // G. C. Greubel, Jun 01 2018
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Mathematica
LinearRecurrence[{12,-36}, {10,90}, 30] (* or *) Table[5*n*6^(n-2), {n,2,30}] (* G. C. Greubel, Jun 01 2018 *) -
PARI
for(n=2,30, print1(5*n*6^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
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)