A173188 a(n) = binomial(n + 5, 5)*9^n.

1, 54, 1701, 40824, 826686, 14880348, 245525742, 3788111448, 55401129927, 775615818978, 10470813556203, 137072468372112, 1747673971744428, 21778706417122872, 266011342666286508, 3192136111995438096, 37707107822946112509, 439176902879019428046

Offset: 0

Author

Zerinvary Lajos, Feb 12 2010

Keywords

• nonn
• easy

Comments

Number of n-permutations (n>=5) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly five (5) u's.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (54,-1215,14580,-98415,354294,-531441).

Crossrefs

Cf. A081139, A173000, A173187.

Programs

Magma

[Binomial(n+5, 5)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011

Mathematica

Table[Binomial[n + 5, 5]*9^n, {n, 0, 20}]

Formula

a(n) = C(n + 5, 5)*9^n.

From Amiram Eldar, Aug 28 2022: (Start)

Sum_{n>=0} 1/a(n) = 184320*log(9/8) - 86835/4.

Sum_{n>=0} (-1)^n/a(n) = 450000*log(10/9) - 189645/4. (End)