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A159740
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Number of permutations of 9 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
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8
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18, 270, 3600, 45000, 540000, 6300000, 72000000, 810000000, 9000000000, 99000000000, 1080000000000, 11700000000000, 126000000000000, 1350000000000000, 14400000000000000, 153000000000000000
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OFFSET
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2,1
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LINKS
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FORMULA
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a(n) = (copies*n)*(copies+1)^(n-2).
a(n) = 9*n*10^(n-2).
G.f.: x^2*(18-90*x)/(1-20*x+100*x^2).
E.g.f.: 9*x*exp(10*x)/10. (End)
Sum_{n>=2} 1/a(n) = (100/9)*log(10/9) - 10/9.
Sum_{n>=2} (-1)^n/a(n) = 10/9 - (100/9)*log(11/10). (End)
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MATHEMATICA
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LinearRecurrence[{20, -100}, {18, 270}, 30] (* or *) Table[9*n*10^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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