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A159739 Number of permutations of 8 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum. 9
16, 216, 2592, 29160, 314928, 3306744, 34012224, 344373768, 3443737680, 34093003032, 334731302496, 3263630199336, 31632108085872, 305023899399480, 2928229434235008, 28001193964872264, 266834907194665104, 2534931618349318488, 24015141647519859360 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 02:28 EST 2022. Contains 358431 sequences. (Running on oeis4.)