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

0,9

Links

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

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

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 *)

Prog

(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

Crossrefs

Column k=4 of A263789.

Sequence in context: A283346 A252348 A252522 * A186917 A185801 A170776

Adjacent sequences: A159709 A159710 A159711 * A159713 A159714 A159715

Keyword

nonn,easy

Author

R. H. Hardin, Apr 20 2009

Extensions

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

Status

approved