A159734 Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 2 local maxima.
80, 8520, 659560, 46412200, 3121135440, 203933233280, 13051880894720, 822269693093760, 51163456598214400, 3151668992962800640, 192538324414433556480, 11680658351228331345920, 704433549821153777192960, 42266012989435750480281600, 2524689842570106278817955840
Offset: 2
Links
- Andrew Howroyd, Table of n, a(n) for n = 2..200
- Index entries for linear recurrences with constant coefficients, signature (130,-5260,68760,-362880,677376).
Programs
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PARI
a(n) = {n*(23^2*56^(n-2) + 21*6^(n-2) - 75*n*6^(n-2))/10} \\ Andrew Howroyd, May 10 2020 -
PARI
Vec(40*x^2*(2 + 3*x)*(1 - 25*x - 303*x^2 + 252*x^3) / ((1 - 6*x)^3*(1 - 56*x)^2) + O(x^18)) \\ Colin Barker, Jul 16 2020
Formula
a(n) = n*(23^2*56^(n-2) + 21*6^(n-2) - 75*n*6^(n-2))/10. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: 40*x^2*(2 + 3*x)*(1 - 25*x - 303*x^2 + 252*x^3) / ((1 - 6*x)^3*(1 - 56*x)^2).
a(n) = 130*a(n-1) - 5260*a(n-2) + 68760*a(n-3) - 362880*a(n-4) + 677376*a(n-5) for n>6.
(End)
Extensions
Terms a(7) and beyond from Andrew Howroyd, May 09 2020