login
Expansion of x + sqrt(1-2x-3x^2).
2

%I #12 Jan 30 2020 21:29:16

%S 1,0,-2,-2,-4,-8,-18,-42,-102,-254,-646,-1670,-4376,-11596,-31022,

%T -83670,-227268,-621144,-1706934,-4713558,-13072764,-36398568,

%U -101704038,-285095118,-801526446,-2259520830,-6385455594,-18086805002

%N Expansion of x + sqrt(1-2x-3x^2).

%C a(n+2) = -2*A001006(n). Hankel transform is (-1)^n*A168057(n).

%C Essentially the same as A167022. - _R. J. Mathar_, Nov 18 2009

%H G. C. Greubel, <a href="/A168058/b168058.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 0^n - 2*Sum_{k=0..floor((n-2)/2)} C(n-2,2k)*A000108(k).

%F D-finite with recurrence: n*a(n) +(-2*n+3)*a(n-1) +3*(-n+3)*a(n-2)=0. - _R. J. Mathar_, Jan 23 2020

%e 1 - 2*x^2 - 2*x^3 - 4*x^4 - 8*x^5 - 18*x^6 - 42*x^7 - 102*x^8 - 254*x^9 - ...

%t CoefficientList[Series[x + Sqrt[1 - 2 x - 3 x^2], {x, 0, 50}], x] (* _G. C. Greubel_, Jul 08 2016 *)

%Y Cf. A168055.

%K easy,sign

%O 0,3

%A _Paul Barry_, Nov 17 2009