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A159738 Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum. 8
14, 168, 1792, 17920, 172032, 1605632, 14680064, 132120576, 1174405120, 10334765056, 90194313216, 781684047872, 6734508720128, 57724360458240, 492581209243648, 4186940278571008, 35465847065542656, 299489375220137984 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
LINKS
FORMULA
a(n) = (copies*n)*(copies+1)^(n-2).
From G. C. Greubel, Jun 01 2018: (Start)
a(n) = 7*n*8^(n-2).
a(n) = 16*a(n-1) - 64*a(n-2).
G.f.: x^2*(14-56*x)/(1-16*x+64*x^2).
E.g.f.: 7*x*exp(8*x)/8. (End)
From Amiram Eldar, May 16 2022: (Start)
Sum_{n>=2} 1/a(n) = (64/7)*log(8/7) - 8/7.
Sum_{n>=2} (-1)^n/a(n) = 8/7 - (64/7)*log(9/8). (End)
MATHEMATICA
LinearRecurrence[{16, -64}, {14, 168}, 30] (* or *) Table[7*n*8^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)
PROG
(PARI) for(n=2, 30, print1(7*n*8^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
(Magma) I:=[14, 168]; [n le 2 select I[n] else 16*Self(n-1) - 64*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 01 2018
CROSSREFS
Sequence in context: A218089 A273587 A125449 * A062148 A200164 A199529
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 20 2009
STATUS
approved

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Last modified June 13 00:21 EDT 2024. Contains 373362 sequences. (Running on oeis4.)