A159711 Number of permutations of 1..n arranged in a circle with exactly 3 local maxima.

0, 0, 0, 0, 0, 0, 96, 1904, 23040, 221184, 1858560, 14353152, 104742912, 734769152, 5010432000, 33464217600, 220066480128, 1430279159808, 9212045819904, 58914039332864, 374665295953920, 2371935399837696, 14960708435312640, 94072038170296320, 589975504803594240

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (32,-444,3504,-17328,55680,-116288,152320,-113664,36864).

Formula

G.f.: -16*(144*x^4-444*x^3+296*x^2-73*x+6)*x^6 / ((6*x-1)^2 *(4*x-1)^3 *(2*x-1)^4). - Alois P. Heinz, Oct 26 2015

a(n) = 1/3*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2) for n>1. - Colin Barker, Oct 26 2015

Mathematica

Table[(1/3)*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2), {n, 0, 30}] (* G. C. Greubel, Jun 01 2018 *)

Prog

(PARI) a(n) = if(n==1, 0, 1/3*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n +6*n^2)) \\ Colin Barker, Oct 26 2015
(PARI) concat(vector(6), Vec(-16*x^6*(144*x^4-444*x^3+296*x^2-73*x+6)/(
(2*x-1)^4*(4*x-1)^3*(6*x-1)^2) + O(x^30))) \\ Colin Barker, Oct 26 2015
(Magma) [(1/3)*2^(-6+n)*n*(15+3*2^(1+n)+3^n-3*(8+2^n)*n+6*n^2): n in [0..30]]; // G. C. Greubel, Jun 01 2018

Crossrefs

Column k=3 of A263789.

Sequence in context: A064243 A001667 A093984 * A268636 A233153 A204624

Adjacent sequences: A159708 A159709 A159710 * A159712 A159713 A159714

Keyword

nonn,easy

Author

R. H. Hardin, Apr 20 2009

Extensions

a(17)-a(24) from Alois P. Heinz, Oct 26 2015

Status

approved