A159739 Number of permutations of 8 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

16, 216, 2592, 29160, 314928, 3306744, 34012224, 344373768, 3443737680, 34093003032, 334731302496, 3263630199336, 31632108085872, 305023899399480, 2928229434235008, 28001193964872264, 266834907194665104, 2534931618349318488, 24015141647519859360

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 (18,-81).

Formula

a(n) = (copies*n)*(copies+1)^(n-2) with copies = 8.

a(n) = 8*n*9^(n-2).

From Colin Barker, Feb 26 2018: (Start)

G.f.: 8*x^2*(2 - 9*x) / (1 - 9*x)^2.

a(n) = 18*a(n-1) - 81*a(n-2) for n>3.

(End)

From Amiram Eldar, May 16 2022: (Start)

Sum_{n>=2} 1/a(n) = (81/8)*log(9/8) - 9/8.

Sum_{n>=2} (-1)^n/a(n) = 9/8 - (81/8)*log(10/9). (End)

Mathematica

LinearRecurrence[{18, -81}, {16, 216}, 30] (* G. C. Greubel, Jun 01 2018 *)

Prog

(PARI) Vec(8*x^2*(2 - 9*x) / (1 - 9*x)^2 + O(x^25)) \\ Colin Barker, Feb 26 2018
(Magma) I:=[16, 216]; [n le 2 select I[n] else 18*Self(n-1) - 81*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 01 2018

Crossrefs

Cf. A159715, A159721, A159727, A159733, A159736, A159738, A159740.

Sequence in context: A239096 A269290 A297098 * A181247 A138454 A235758

Adjacent sequences: A159736 A159737 A159738 * A159740 A159741 A159742

Keyword

nonn,easy

Author

R. H. Hardin, Apr 20 2009

Status

approved