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

%S 1,1,7,13,73,187,895,2737,11923,40333,166753,598111,2404309,8926651,

%T 35365651,134054005,527360581,2024611351,7940840719,30733601689,

%U 120439122811,468630460885,1836912780541,7173754477099,28140632060899

%N Expansion of 1/sqrt(1-2x-11x^2+12x^3).

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

%H Vincenzo Librandi, <a href="/A098478/b098478.txt">Table of n, a(n) for n = 0..200</a>

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

%F D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) + 11*(n-1)*a(n-2) - 6*(2*n-3)*a(n-3). - _Vaclav Kotesovec_, Jun 23 2014

%F a(n) ~ 2^(2*n+2) / sqrt(21*Pi*n). - _Vaclav Kotesovec_, Jun 23 2014

%t CoefficientList[Series[1/Sqrt[1-2*x-11*x^2+12*x^3], {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jun 23 2014 *)

%Y Cf. A026569, A098477.

%K nonn

%O 0,3

%A _Paul Barry_, Sep 10 2004