A159736 Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

12, 126, 1176, 10290, 86436, 705894, 5647152, 44471322, 345888060, 2663338062, 20338217928, 154231485954, 1162668124884, 8720010936630, 65109414993504, 484251274014186, 3589156501516908, 26519878594541598, 195409631749253880

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 (14,-49).

Formula

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

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

a(n) = 6*n*7^(n-2).

a(n) = 14*a(n-1) - 49*a(n-2).

G.f.: x^2*(12-42*x)/(1-14*x+49*x^2).

E.g.f.: 6*x*exp(7*x)/7. (End)

From Amiram Eldar, May 16 2022: (Start)

Sum_{n>=2} 1/a(n) = (49/6)*log(7/6) - 7/6.

Sum_{n>=2} (-1)^n/a(n) = 7/6 - (49/6)*log(8/7). (End)

Mathematica

LinearRecurrence[{14, -49}, {12, 126}, 30] (* or *) Table[6*n*7^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)

Prog

(PARI) for(n=2, 30, print1(6*n*7^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
(Magma) I:=[12, 126]; [n le 2 select I[n] else 14*Self(n-1) - 49*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 01 2018

Crossrefs

Cf. A159715, A159721, A159727, A159733, A159738, A159739, A159740.

Sequence in context: A015792 A343769 A348463 * A004991 A228008 A101602

Adjacent sequences: A159733 A159734 A159735 * A159737 A159738 A159739

Keyword

nonn

Author

R. H. Hardin, Apr 20 2009

Status

approved