A173192 a(n) = binomial(n + 7, 7)*9^n.

1, 72, 2916, 87480, 2165130, 46766808, 911952756, 16415149608, 277005649635, 4432090394160, 67810983030648, 998670840996816, 14231059484204628, 197045439012064080, 2660113426662865080, 35113497231949819056, 454280870438350784037, 5772039294981398197176

Offset: 0

Author

Zerinvary Lajos, Feb 12 2010

Keywords

• nonn
• easy

Comments

Number of n-permutations (n>=7) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 7 u's.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (72,-2268,40824,-459270,3306744,-14880348,38263752,-43046721).

Crossrefs

Cf. A081139, A173000, A173187, A173188, A173191.

Programs

Magma

[Binomial(n+7, 7)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011

Maple

A173192:=n->binomial(n+7,7)*9^n: seq(A173192(n), n=0..25); # Wesley Ivan Hurt, Jul 24 2017

Mathematica

Table[Binomial[n + 7, 7]*9^n, {n, 0, 20}]

Formula

a(n) = C(n + 7, 7)*9^n.

From Amiram Eldar, Aug 29 2022: (Start)

Sum_{n>=0} 1/a(n) = 16515072*log(9/8) - 19451943/10.

Sum_{n>=0} (-1)^n/a(n) = 63000000*log(10/9) - 13275423/2. (End)