A159738 Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.

14, 168, 1792, 17920, 172032, 1605632, 14680064, 132120576, 1174405120, 10334765056, 90194313216, 781684047872, 6734508720128, 57724360458240, 492581209243648, 4186940278571008, 35465847065542656, 299489375220137984

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 (16,-64).

Formula

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

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

a(n) = 7*n*8^(n-2).

a(n) = 16*a(n-1) - 64*a(n-2).

G.f.: x^2*(14-56*x)/(1-16*x+64*x^2).

E.g.f.: 7*x*exp(8*x)/8. (End)

From Amiram Eldar, May 16 2022: (Start)

Sum_{n>=2} 1/a(n) = (64/7)*log(8/7) - 8/7.

Sum_{n>=2} (-1)^n/a(n) = 8/7 - (64/7)*log(9/8). (End)

Mathematica

LinearRecurrence[{16, -64}, {14, 168}, 30] (* or *) Table[7*n*8^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *)

Prog

(PARI) for(n=2, 30, print1(7*n*8^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
(Magma) I:=[14, 168]; [n le 2 select I[n] else 16*Self(n-1) - 64*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 01 2018

Crossrefs

Cf. A159715, A159721, A159727, A159733, A159736, A159739, A159740.

Sequence in context: A218089 A273587 A125449 * A062148 A200164 A199529

Adjacent sequences: A159735 A159736 A159737 * A159739 A159740 A159741

Keyword

nonn

Author

R. H. Hardin, Apr 20 2009

Status

approved