A098481 - OEIS

%I #23 Jan 30 2020 21:29:15

%S 1,1,1,7,19,37,115,361,937,2599,7777,22195,62701,182647,531829,

%T 1534903,4461571,13034917,38015899,110994193,325011151,952442557,

%U 2792471239,8198275933,24093817531,70852613041,208516575043,614145137137

%N Expansion of 1/sqrt((1-x)^2 - 12*x^3).

%C 1/sqrt((1-x)^2 - 4*r*x^3) expands to Sum_{k=0..floor(n/2)} binomial(n-k, k)*binomial(n-2k, k)*r^k.

%H G. C. Greubel and Vincenzo Librandi, <a href="/A098481/b098481.txt">Table of n, a(n) for n = 0..1000</a>(terms 0..200 from Vincenzo Librandi)

%F a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*binomial(n-2k, k)*3^k.

%F D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) + 6*(2*n-3)*a(n-3). - _Vaclav Kotesovec_, Jun 23 2014

%F a(n) ~ 3^(n+1) / (4*sqrt(Pi*n)). - _Vaclav Kotesovec_, Jun 23 2014

%t CoefficientList[Series[1/Sqrt[(1-x)^2-12x^3],{x,0,40}],x] (* _Harvey P. Dale_, Jun 02 2011 *)

%o (PARI) Vec(1/sqrt((1-x)^2 - 12*x^3) + O(x^50)) \\ _G. C. Greubel_, Jan 30 2017

%Y Cf. A098479, A098480.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Sep 10 2004