A169796 Expansion of ((1-x)/(1-2x))^9.

1, 9, 54, 264, 1134, 4446, 16272, 56412, 187137, 598417, 1854882, 5597172, 16498632, 47638512, 135048672, 376592064, 1034663040, 2804590080, 7509232640, 19880294400, 52088352768, 135173578752, 347680161792, 886900948992, 2245014454272, 5641949085696

Offset

0,2

Comments

a(n) is the number of weak compositions of n with exactly 8 parts equal to 0. - Milan Janjic, Jun 27 2010

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Nickolas Hein, Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.

M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.

Index entries for linear recurrences with constant coefficients, signature (18, -144, 672, -2016, 4032, -5376, 4608, -2304, 512).

Formula

G.f.: ((1-x)/(1-2*x))^9.

For n > 0, a(n) = 2^(n-16)*(n+8)*(n^7 + 100*n^6 + 3778*n^5 + 68056*n^4 + 606961*n^3 + 2543284*n^2 + 4524300*n + 2575440)/315. - Bruno Berselli, Aug 07 2011

Mathematica

CoefficientList[Series[((1 - x)/(1 - 2 x))^9, {x, 0, 25}], x] (* Michael De Vlieger, Oct 15 2018 *)

Crossrefs

Cf. for ((1-x)/(1-2x))^k: A011782, A045623, A058396, A062109, A169792-A169797; a row of A160232.

Sequence in context: A282920 A023008 A079817 * A359722 A027472 A022637

Adjacent sequences: A169793 A169794 A169795 * A169797 A169798 A169799

Keyword

nonn,easy

Author

N. J. A. Sloane, May 15 2010

Status

approved