A159740 Number of permutations of 9 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

18, 270, 3600, 45000, 540000, 6300000, 72000000, 810000000, 9000000000, 99000000000, 1080000000000, 11700000000000, 126000000000000, 1350000000000000, 14400000000000000, 153000000000000000

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 (20,-100).

Formula

a(n) = (copies*n)*(copies+1)^(n-2).

From G. C. Greubel, Jun 01 2018: (Start)

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)

From Amiram Eldar, May 16 2022: (Start)

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)

Mathematica

LinearRecurrence[{20, -100}, {18, 270}, 30] (* or *) Table[9*n*10^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)

Prog

(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

Crossrefs

Cf. A159715, A159721, A159727, A159733, A159736, A159738, A159739.

Sequence in context: A273589 A076693 A083445 * A115903 A004357 A249598

Adjacent sequences: A159737 A159738 A159739 * A159741 A159742 A159743

Keyword

nonn

Author

R. H. Hardin, Apr 20 2009

Status

approved