|
|
A169794
|
|
Expansion of ((1-x)/(1-2*x))^7.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|