A159710 Number of permutations of 1..n arranged in a circle with exactly 2 local maxima.

0, 0, 0, 0, 8, 80, 528, 2912, 14592, 69120, 316160, 1413632, 6223872, 27103232, 117067776, 502456320, 2145517568, 9122349056, 38644678656, 163186343936, 687144960000, 2886107922432, 12094385684480, 50577004298240, 211105074905088, 879606785638400

Offset: 0

Author

R. H. Hardin, Apr 20 2009

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14,-76,200,-256,128).

Crossrefs

Column k=2 of A263789.

Programs

Magma

[0,0] cat [2^(-5+n)*(4+2^n-4*n)*n: n in [2..30]]; // G. C. Greubel, Jun 02 2018

Mathematica

LinearRecurrence[{14,-76,200,-256,128},{0,0,0,0,8,80,528},30] (* Harvey P. Dale, Sep 23 2017 *)
Join[{0,0}, Table[2^(-5+n)*(4+2^n-4*n)*n, {n, 2, 30}]] (* G. C. Greubel, Jun 02 2018 *)

PARI

concat([0, 0, 0, 0], Vec(-8*(2*x^2-4*x+1)*x^4 / ((4*x-1)^2*(2*x -1)^3) + O(x^100))) \\ Altug Alkan, Oct 26 2015

PARI

a(n) = if(n==1, 0, 2^(-5+n)*(4+2^n-4*n)*n) \\ Colin Barker, Oct 26 2015

Formula

G.f.: -8*(2*x^2-4*x+1)*x^4 / ((4*x-1)^2*(2*x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009

a(n) = 2^(-5+n)*(4+2^n-4*n)*n for n>1. - Colin Barker, Oct 26 2015

a(n) = 14*a(n-1) - 76*a(n-2) + 200*a(n-3) - 256*a(n-4) + 128*a(n-5). - Wesley Ivan Hurt, Aug 04 2025

Extensions

More terms from Alois P. Heinz, Oct 26 2015