A169795 Expansion of ((1-x)/(1-2x))^8.
1, 8, 44, 200, 806, 2984, 10364, 34232, 108545, 332688, 990736, 2878144, 8182432, 22823680, 62595328, 169090048, 450568960, 1185832960, 3085885440, 7947714560, 20275478528, 51272351744, 128605356032, 320145981440, 791358537728, 1943278714880, 4742573981696
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 (16, -112, 448, -1120, 1792, -1792, 1024, -256).
Crossrefs
Programs
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Mathematica
CoefficientList[Series[((1-x)/(1-2x))^8,{x,0,30}],x] (* Harvey P. Dale, Nov 24 2016 *)
Formula
G.f.: ((1-x)/(1-2*x))^8.
For n > 0, a(n) = 2^(n-12)*(n+9) * (n^6 + 75*n^5 + 1999*n^4 + 23169*n^3 + 115768*n^2 + 232284*n + 142800)/315. - Bruno Berselli, Aug 07 2011
Comments