A173155 a(n) = binomial(n + 5, 5) * 8^n.

1, 48, 1344, 28672, 516096, 8257536, 121110528, 1660944384, 21592276992, 268703891456, 3224446697472, 37520834297856, 425236122042368, 4710307813392384, 51140484831117312, 545498504865251328, 5727734301085138944, 59298896293587320832, 606166495445559279616

Offset: 0

Author

Zerinvary Lajos, Feb 11 2010

Keywords

• nonn
• easy

Comments

With a different offset, number of n-permutations (n>=5) of 9 objects: p, r, s, t, u, v, z, x, y 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 (48,-960,10240,-61440,196608,-262144).

Crossrefs

Cf. A081138, A140802, A175210, A140406, A053107, A141054.

Programs

Magma

[8^n* Binomial(n+5, 5): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

Mathematica

Table[Binomial[n + 5, 5]*8^n, {n, 0, 20}]

Formula

a(n) = C(n + 5, 5)*8^n, n>=0.

G.f.: 1/(1-8*x)^6. - Vincenzo Librandi, Oct 16 2011

From Amiram Eldar, Aug 29 2022: (Start)

Sum_{n>=0} 1/a(n) = 96040*log(8/7) - 38470/3.

Sum_{n>=0} (-1)^n/a(n) = 262440*log(9/8) - 30910. (End)