A140325 a(n) = binomial(n+8,8) * 2^n.

1, 18, 180, 1320, 7920, 41184, 192192, 823680, 3294720, 12446720, 44808192, 154791936, 515973120, 1666990080, 5239111680, 16066609152, 48199827456, 141764198400, 409541017600, 1163958681600, 3259084308480, 9001280471040

Offset: 0

Author

Zerinvary Lajos, Jun 23 2008

Keywords

• nonn
• easy

Comments

With a different offset, number of n-permutations (n>=8) of 3 objects: u, v, z with repetition allowed, containing exactly eight (8) u's. See example.

Number of 8D hypercubes in an (n+8)-dimensional hypercube. [Zerinvary Lajos, Jan 29 2010]

Examples

			Example: a(1)=18 because we have uuuuuuuuv, uuuuuuuvu, uuuuuuvuu, uuuuuvuuu, uuuuvuuuu, uuuvuuuuu, uuvuuuuuu, uvuuuuuuu, vuuuuuuuu, uuuuuuuuz, uuuuuuuzu, uuuuuuzuu, uuuuuzuuu, uuuuzuuuu, uuuzuuuuu, uuzuuuuuu, uzuuuuuuu and zuuuuuuu.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Milan Janjic and Boris Petkovic, A Counting Function, arXiv:1301.4550 [math.CO], 2013.
• Index entries for linear recurrences with constant coefficients, signature (18,-144,672,-2016,4032,-5376,4608,-2304,512).

Crossrefs

Cf. A038207, A054851.

Programs

Magma

[2^n*Binomial(n+8, 8): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011

Maple

seq(binomial(n+8,8)*2^n,n=0..28);

Mathematica

Table[Binomial[n + 8, 8] 2^n, {n, 0, 20}] (* Zerinvary Lajos, Jan 29 2010 *)

Formula

a(n) = A038207(n+8,8).

G.f.: 1/(1-2*x)^9. - R. J. Mathar, Feb 11 2010

a(n) = 2*a(n-1) + A054851(n-1). - Ruskin Harding, May 12 2013

a(n) = Sum_{i=8..n+8} binomial(i,8)*binomial(n+8,i). Example: for n=6, a(6) = 1*3003 + 9*2002 + 45*1001 + 165*364 + 495*91 + 1287*14 + 3003*1 = 192192. - Bruno Berselli, Mar 23 2018

From Amiram Eldar, Jan 07 2022: (Start)

Sum_{n>=0} 1/a(n) = 1276/105 - 16*log(2).

Sum_{n>=0} (-1)^n/a(n) = 34992*log(3/2) - 496548/35. (End)