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
Keywords
Links
- R. H. Hardin, Table of n, a(n) for n=2..100
- Index entries for linear recurrences with constant coefficients, signature (14,-49).
Programs
-
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
-
Mathematica
LinearRecurrence[{14,-49}, {12, 126}, 30] (* or *) Table[6*n*7^(n-2), {n, 2, 30}] (* G. C. Greubel, Jun 01 2018 *) -
PARI
for(n=2, 30, print1(6*n*7^(n-2), ", ")) \\ G. C. Greubel, Jun 01 2018
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)