A169794 Expansion of ((1-x)/(1-2*x))^7.

1, 7, 35, 147, 553, 1925, 6321, 19825, 59906, 175504, 500864, 1397536, 3823680, 10282496, 27230464, 71129856, 183518720, 468213760, 1182433280, 2958376960, 7338426368, 18059821056, 44120473600, 107055742976, 258122317824, 618683957248, 1474700509184

Offset

0,2

Comments

a(n) is the number of weak compositions of n with exactly 6 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 (14, -84, 280, -560, 672, -448, 128).

Formula

G.f.: ((1-x)/(1-2*x))^7.

For n > 0, a(n) = 2^(n-11)*(n+3)*(n+6)*(n^4 + 54*n^3 + 931*n^2 + 5454*n + 5080)/45. - Bruno Berselli, Aug 07 2011

Maple

seq(coeff(series(((1-x)/(1-2*x))^7, x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 16 2018

Mathematica

CoefficientList[Series[((1 - x)/(1 - 2 x))^7, {x, 0, 26}], x] (* Michael De Vlieger, Oct 15 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(((1-x)/(1-2*x))^7) \\ G. C. Greubel, Oct 16 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(((1-x)/(1-2*x))^7)); // G. C. Greubel, Oct 16 2018

Crossrefs

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

Sequence in context: A160539 A023006 A001875 * A240418 A211843 A121163

Adjacent sequences: A169791 A169792 A169793 * A169795 A169796 A169797

Keyword

nonn,easy

Author

N. J. A. Sloane, May 15 2010

Status

approved