A098580 Expansion of (sqrt(1-8*x)-4*x)/sqrt(1-8*x).

1, -4, -16, -96, -640, -4480, -32256, -236544, -1757184, -13178880, -99573760, -756760576, -5778898944, -44304891904, -340806860800, -2629081497600, -20331563581440, -157569617756160, -1223481737871360, -9515969072332800, -74124390668697600

Offset: 0

Author

Paul Barry, Sep 16 2004

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A059304.

Programs

Magma

Q:=Rationals(); R:=PowerSeriesRing(Q, 40); Coefficients(R!((sqrt(1-8*x)-4*x)/sqrt(1-8*x))) // G. C. Greubel, Feb 03 2018

Mathematica

CoefficientList[Series[(Sqrt[1-8x]-4x)/Sqrt[1-8x],{x,0,20}],x] (* Harvey P. Dale, May 06 2017 *)

PARI

x='x+O('x^30); Vec((sqrt(1-8*x)-4*x)/sqrt(1-8*x)) \\ G. C. Greubel, Feb 03 2018

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