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%I #19 Jan 29 2019 10:07:06
%S 2,0,1,2,4,9,22,56,146,388,1048,2869,7942,22192,62510,177308,506008,
%T 1451866,4185788,12119696,35227748,102753800,300672368,882373261,
%U 2596389190,7658677856,22642421206,67081765932,199128719896,592179010350,1764044315540
%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.
%H G. C. Greubel, <a href="/A025247/b025247.txt">Table of n, a(n) for n = 1..1000</a>
%H Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Barry/barry321.html">Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices</a>, Journal of Integer Sequences, 19, 2016, #16.3.5.
%F G.f.: (1+2*x-sqrt(1-4*x+4*x^2-4*x^3))/2. - _Michael Somos_, Jun 08 2000
%F Conjecture: n*a(n) +2*(3-2*n)*a(n-1) +4*(n-3)*a(n-2) +2*(9-2*n)*a(n-3)=0. - _R. J. Mathar_, Aug 14 2012
%t Rest[CoefficientList[Series[(1+2x-Sqrt[1-4x+4x^2-4x^3])/2, {x,0,40}], x]] (* _Harvey P. Dale_, Apr 23 2011 *)
%o (PARI) a(n)=polcoeff((2*x-sqrt(1-4*x+4*x^2-4*x^3+x*O(x^n)))/2,n)
%K nonn
%O 1,1
%A _Clark Kimberling_
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