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A140325 a(n) = binomial(n+8,8) * 2^n. 13
1, 18, 180, 1320, 7920, 41184, 192192, 823680, 3294720, 12446720, 44808192, 154791936, 515973120, 1666990080, 5239111680, 16066609152, 48199827456, 141764198400, 409541017600, 1163958681600, 3259084308480, 9001280471040 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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]
LINKS
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).
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)
EXAMPLE
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.
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 *)
PROG
(Magma) [2^n*Binomial(n+8, 8): n in [0..30]]; // Vincenzo Librandi, Oct 14 2011
CROSSREFS
Sequence in context: A121038 A341370 A004410 * A199299 A155669 A160954
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 23 2008
STATUS
approved

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Last modified March 2 19:19 EST 2024. Contains 370498 sequences. (Running on oeis4.)