A173000 a(n) = binomial(n + 4, 4)*9^n.

1, 45, 1215, 25515, 459270, 7440174, 111602610, 1578379770, 21308126895, 277005649635, 3490271185401, 42835146366285, 514021756395420, 6049640671423020, 70002984912180660, 798034027998859524, 8977882814987169645, 99812932472504415465, 1097942257197548570115

Offset: 0

Author

Zerinvary Lajos, Feb 07 2010

Keywords

• nonn
• easy

Comments

Number of n-permutations (n>=4) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 4 u's.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (45,-810,7290,-32805,59049).

Crossrefs

Cf. A000332, A001019.

Programs

Magma

[Binomial(n+4, 4)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011

Maple

A173000:=n->binomial(n+4,4)*9^n: seq(A173000(n), n=0..25); # Wesley Ivan Hurt, Jul 24 2017

Mathematica

Table[Binomial[n + 4, 4]*9^n, {n, 0, 20}]

PARI

a(n)=binomial(n+4,4)*9^n \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 1/(1-9*x)^5. - R. J. Mathar, Dec 21 2011

a(n) = 45*a(n-1)-810*a(n-2)+7290*a(n-3)-32805*a(n-4)+59049*a(n-5). - Wesley Ivan Hurt, Apr 21 2021

From Amiram Eldar, Aug 28 2022: (Start)

Sum_{n>=0} 1/a(n) = 2172 - 18432*log(9/8).

Sum_{n>=0} (-1)^n/a(n) = 36000*log(10/9) - 3792. (End)

a(n) = A000332(n+4)*A001019(n). - Michel Marcus, Aug 28 2022