|
|
A098580
|
|
Expansion of (sqrt(1-8*x)-4*x)/sqrt(1-8*x).
|
|
1
|
|
|
1, -4, -16, -96, -640, -4480, -32256, -236544, -1757184, -13178880, -99573760, -756760576, -5778898944, -44304891904, -340806860800, -2629081497600, -20331563581440, -157569617756160, -1223481737871360, -9515969072332800, -74124390668697600
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1-4*x/sqrt(1-8*x).
a(0)=1, a(n) = -2^(n+1)*(2*(n-1))!/(n-1)!^2.
D-finite with recurrence: (n-1)*a(n) +4*(3-2*n)*a(n-1)=0. - R. J. Mathar, Sep 26 2012
|
|
MATHEMATICA
|
CoefficientList[Series[(Sqrt[1-8x]-4x)/Sqrt[1-8x], {x, 0, 20}], x] (* Harvey P. Dale, May 06 2017 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec((sqrt(1-8*x)-4*x)/sqrt(1-8*x)) \\ G. C. Greubel, Feb 03 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((sqrt(1-8*x)-4*x)/sqrt(1-8*x))) // G. C. Greubel, Feb 03 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|