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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.
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%I #12 Jun 15 2022 10:48:05

%S 3,2,6,22,90,394,1806,8558,41586,206098,1037718,5293446,27297738,

%T 142078746,745387038,3937603038,20927156706,111818026018,600318853926,

%U 3236724317174,17518619320890,95149655201962,518431875418926,2832923350929742

%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.

%F G.f.: (1+3*x-sqrt(1-6*x+x^2))/2. - _Michael Somos_, Jun 08 2000

%F Conjecture: n*a(n) +3*(-2*n+3)*a(n-1) +(n-3)*a(n-2)=0. - _R. J. Mathar_, Feb 25 2015

%t Rest[CoefficientList[Series[(1+3x-Sqrt[1-6x+x^2])/2,{x,0,40}],x]] (* _Harvey P. Dale_, Aug 26 2013 *)

%o (PARI) a(n)=polcoeff((1+3*x-sqrt(1-6*x+x^2+x*O(x^n)))/2,n)

%Y Essentially same as A006318.

%K nonn

%O 1,1

%A _Clark Kimberling_