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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 15 2010
STATUS
approved