A152518 1/36 of the number of permutations of 8 indistinguishable copies of 1..n with exactly 2 local maxima.
0, 7, 1290, 214713, 35450244, 5849546139, 965177888238, 159254380788525, 26276973131433672, 4335700569742873071, 715390594038180275346, 118039448016603095674977, 19476508922742491987034060, 3213623972252540268102877443, 530247955421669426384081722614
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (183,-3051,13365).
Programs
-
PARI
a(n) = {(97*165^(n-1) - 97*9^(n-1) - 104*(n-1)*9^(n-1))/2028} \\ Andrew Howroyd, May 10 2020 -
PARI
concat(0, Vec(x^2*(7 + 9*x) / ((1 - 9*x)^2*(1 - 165*x)) + O(x^17))) \\ Colin Barker, Jul 18 2020
Formula
a(n) = (97*165^(n-1) - 97*9^(n-1) - 104*(n-1)*9^(n-1))/2028. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 18 2020: (Start)
G.f.: x^2*(7 + 9*x) / ((1 - 9*x)^2*(1 - 165*x)).
a(n) = 183*a(n-1) - 3051*a(n-2) + 13365*a(n-3) for n>3.
(End)
Extensions
Terms a(7) and beyond from Andrew Howroyd, May 10 2020