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