A159727 Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
8, 60, 400, 2500, 15000, 87500, 500000, 2812500, 15625000, 85937500, 468750000, 2539062500, 13671875000, 73242187500, 390625000000, 2075195312500, 10986328125000, 57983398437500, 305175781250000, 1602172851562500
Offset: 2
Links
- R. H. Hardin, Table of n, a(n) for n = 2..100
- Index entries for linear recurrences with constant coefficients, signature (10,-25).
Programs
-
Magma
[ 4*n*5^(n-2) : n in [2..30]]; // G. C. Greubel, Jun 01 2018
-
Mathematica
LinearRecurrence[{10,-25}, {8,60}, 30] (* or *) Table[4*n*5^(n-2), {n,2,30}] (* G. C. Greubel, Jun 01 2018 *) -
PARI
for(n=2, 30, print1(4*n*5^(n-2) , ", ")) \\ G. C. Greubel, Jun 01 2018
Formula
a(n) = (4*n)*(4+1)^(n-2).
From Colin Barker, Mar 23 2018: (Start)
G.f.: 4*x^2*(2 - 5*x) / (1 - 5*x)^2.
a(n) = 10*a(n-1) - 25*a(n-2) for n>3. (End)
E.g.f.: 4*x*exp(5*x)/5. - G. C. Greubel, Jun 01 2018
From Amiram Eldar, May 16 2022: (Start)
Sum_{n>=2} 1/a(n) = (25/4)*log(5/4) - 5/4.
Sum_{n>=2} (-1)^n/a(n) = 5/4 - (25/4)*log(6/5). (End)