%I #18 Jan 30 2020 21:29:16
%S 1,0,3,3,6,12,27,63,153,381,969,2505,6564,17394,46533,125505,340902,
%T 931716,2560401,7070337,19609146,54597852,152556057,427642677,
%U 1202289669,3389281245,9578183391,27130207503,77009455428,219023318406,624069834627,1781228354487
%N Expansion of 1 + 3*(1-x-sqrt(1-2*x-3*x^2))/2.
%C Hankel transform is A168072. a(n+2)=3*A000106(n). Another variant is A168076.
%H G. C. Greubel, <a href="/A168073/b168073.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = 0^n+3*Sum_{k=0..floor((n-2)/2)} C(n-2,2k)*A000108(k).
%F D-finite with recurrence: a(n) = ((2*n-3)*a(n-1)+(3*n-9)*a(n-2))/n for n>=3, a(0)=1, a(1)=0, a(2)=3. - _Sergei N. Gladkovskii_, Jul 16 2012
%t CoefficientList[Series[1 + 3*(1 - x - Sqrt[1 - 2*x - 3*x^2])/2, {x, 0, 50}], x] (* _G. C. Greubel_, Jul 09 2016 *)
%Y Cf. A168055, A168049.
%Y Cf. A000106, A168072, A168076.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Nov 18 2009