A159713 Number of permutations of 1..n arranged in a circle with exactly 5 local maxima.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 79360, 3891712, 108736512, 2283154432, 40155709440, 625974681600, 8946380963840, 119830778347520, 1527173964103680, 18720292422287360, 222492157815029760, 2579416038567051264, 29306002590306140160, 327494389862875791360

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

Crossrefs

Column k=5 of A263789.

Programs

PARI

concat(vector(10), Vec(-512*(232243200*x^11 -1275402240*x^10 [phone]*x^9 -2074564992*x^8 [phone]*x^7 -439150208*x^6 [phone]*x^5 -19636984*x^4 +2325314*x^3 -177676*x^2 +7899*x -155)*x^10 / ((10*x-1)^2 *(8*x-1)^3 *(6*x-1)^4 *(4*x-1)^5 *(2*x-1)^6) + O(x^100))) \\ Altug Alkan, Oct 26 2015

Formula

G.f.: -512*(232243200*x^11 -1275402240*x^10 [phone]*x^9 -2074564992*x^8 [phone]*x^7 -439150208*x^6 [phone]*x^5 -19636984*x^4 +2325314*x^3 -177676*x^2 +7899*x -155)*x^10 / ((10*x-1)^2 *(8*x-1)^3 *(6*x-1)^4 *(4*x-1)^5 *(2*x-1)^6). - Alois P. Heinz, Oct 26 2015

Extensions

a(16)-a(23) from Alois P. Heinz, Oct 26 2015