A152513 1/21 of the number of permutations of 6 indistinguishable copies of 1..n with exactly 2 local maxima.
0, 5, 497, 42581, 3584693, 301183841, 25300030889, 2125207418285, 178517461842461, 14995467100301177, 1259619238806161681, 105808016078078472389, 8887873350698981879429, 746581361459780256986513, 62712834362629583374730873, 5267878086460945365330876893
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (98,-1225,4116).
Programs
-
PARI
a(n) = {(61*84^(n-1) - 61*7^(n-1) - 66*(n-1)*7^(n-1))/847} \\ Andrew Howroyd, May 10 2020 -
PARI
Vec(x^2*(5 + 7*x) / ((1 - 7*x)^2*(1 - 84*x)) + O(x^18)) \\ Colin Barker, Jul 16 2020
Formula
a(n) = (61*84^(n-1) - 61*7^(n-1) - 66*(n-1)*7^(n-1))/847. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: x^2*(5 + 7*x) / ((1 - 7*x)^2*(1 - 84*x)).
a(n) = 98*a(n-1) - 1225*a(n-2) + 4116*a(n-3) for n>3.
(End)
Extensions
Terms a(7) and beyond from Andrew Howroyd, May 10 2020