A159712 Number of permutations of 1..n arranged in a circle with exactly 4 local maxima.

0, 0, 0, 0, 0, 0, 0, 0, 2176, 71424, 1372160, 20252672, 255040512, 2891180032, 30447656960, 303926476800, 2914762424320, 27113686958080, 246327423270912, 2196784154673152, 19305427103907840, 167673167523348480, 1442534103145512960, 12315082531044065280

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=4 of A263789.

Programs

Mathematica

CoefficientList[Series[-128*(34560*x^7 -146880*x^6 +173712*x^5 -97304*x^4 +29808*x^3 -5120*x^2 +462*x-17)*x^8 / ((8*x-1)^2 *(6*x-1)^3 *(4*x-1)^4 *(2*x-1)^5), {x, 0, 50}], x] (* G. C. Greubel, Jun 02 2018 *)

PARI

concat(vector(8), Vec(-128*(34560*x^7 -146880*x^6 +173712*x^5 -97304*x^4 +29808*x^3 -5120*x^2 +462*x-17)*x^8 / ((8*x-1)^2 *(6*x-1)^3 *(4*x-1)^4 *(2*x-1)^5) + O(x^100))) \\ Altug Alkan, Oct 26 2015

Formula

G.f.: -128*(34560*x^7 -146880*x^6 +173712*x^5 -97304*x^4 +29808*x^3 -5120*x^2 +462*x-17)*x^8 / ((8*x-1)^2 *(6*x-1)^3 *(4*x-1)^4 *(2*x-1)^5). - Alois P. Heinz, Oct 26 2015

Extensions

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