A152509 1/30 of the number of permutations of 5 indistinguishable copies of 1..n with exactly 2 local maxima.
0, 2, 139, 8036, 452068, 25331360, 1418668912, 79446252224, 4448995583296, 249143789616128, 13952052465406720, 781314939695363072, 43753636633642845184, 2450203651553656365056, 137211404487455350386688, 7683838651300399095726080, 430294964472840921667551232
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (68,-708,2016).
Programs
-
Mathematica
LinearRecurrence[{68,-708,2016},{0,2,139},20] (* Harvey P. Dale, Feb 03 2022 *) -
PARI
a(n) = {(23*56^(n-1) - 23*6^(n-1) - 25*(n-1)*6^(n-1))/500} \\ Andrew Howroyd, May 10 2020 -
PARI
concat(0, Vec(x^2*(2 + 3*x) / ((1 - 6*x)^2*(1 - 56*x)) + O(x^20))) \\ Colin Barker, Jul 16 2020
Formula
a(n) = (23*56^(n-1) - 23*6^(n-1) - 25*(n-1)*6^(n-1))/500. - Andrew Howroyd, May 10 2020
From Colin Barker, Jul 16 2020: (Start)
G.f.: x^2*(2 + 3*x) / ((1 - 6*x)^2*(1 - 56*x)).
a(n) = 68*a(n-1) - 708*a(n-2) + 2016*a(n-3) for n>3.
(End)
Extensions
Terms a(8) and beyond from Andrew Howroyd, May 10 2020