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

0,2

Comments

a(n) is the number of weak compositions of n with exactly 7 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 (16, -112, 448, -1120, 1792, -1792, 1024, -256).

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

Mathematica

CoefficientList[Series[((1-x)/(1-2x))^8, {x, 0, 30}], x] (* Harvey P. Dale, Nov 24 2016 *)

Crossrefs

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

Sequence in context: A277958 A283077 A023007 * A073380 A273603 A270902

Adjacent sequences: A169792 A169793 A169794 * A169796 A169797 A169798

Keyword

nonn,easy

Author

N. J. A. Sloane, May 15 2010

Status

approved