A170932 a(n) = binomial(n + 8, 8)*7^n .

1, 63, 2205, 56595, 1188495, 21630609, 353299947, 5299499205, 74192988870, 980996186170, 12360551945742, 149450309889426, 1743586948709970, 19715944727720430, 216875392004924730, 2327795874186192102, 24441856678955017071, 251607348165713411025

Offset: 0

Author

Zerinvary Lajos, Feb 08 2010

Keywords

• nonn
• easy

Comments

With a different offset, number of n-permutations of 8 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly eight, (8) u's.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (63,-1764,28812,-302526,2117682,-9882516,29647548,-51883209,40353607).

Crossrefs

Cf. A027474, A140107, A139641, A140404, A036226, A050989.

Programs

Magma

[Binomial(n + 8, 8)*7^n: n in [0..20]]; // Vincenzo Librandi, Oct 12 2011

Mathematica

Table[Binomial[n + 8, 8]*7^n, {n, 0, 20}]

Formula

a(n) = C(n + 8, 8)*7^n.

From Amiram Eldar, Aug 29 2022: (Start)

Sum_{n>=0} 1/a(n) = 12082656/5 - 15676416*log(7/6).

Sum_{n>=0} (-1)^n/a(n) = 117440512*log(8/7) - 235229912/15. (End)