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

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (68,-708,2016).

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)

Mathematica

LinearRecurrence[{68, -708, 2016}, {0, 2, 139}, 20] (* Harvey P. Dale, Feb 03 2022 *)

Prog

(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

Crossrefs

Cf. A152494, A334773.

Sequence in context: A329594 A084560 A054681 * A265462 A094482 A265176

Adjacent sequences: A152506 A152507 A152508 * A152510 A152511 A152512

Keyword

nonn,easy

Author

R. H. Hardin, Dec 06 2008

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 10 2020

Status

approved