%I #12 Mar 31 2023 17:10:59
%S 3,1,3,10,36,137,543,2219,9285,39587,171369,751236,3328218,14878455,
%T 67030785,304036170,1387247580,6363044315,29323149825,135700543190,
%U 630375241380,2938391049395,13739779184085,64430797069375,302934667061301
%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+5*x^2))/2 - _Michael Somos_, Jun 08 2000
%F G.f.: (1+3*x - (1-5*x)*G(0))/(2*x), where G(k)= 1 + 4*x*(4*k+1)/( (4*k+2)*(1-x) - 2*x*(1-x)*(2*k+1)*(4*k+3)/(x*(4*k+3) + (1-x)*(k+1)/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 25 2013
%F D-finite with recurrence n*a(n) +3*(-2*n+3)*a(n-1) +5*(n-3)*a(n-2)=0. - _R. J. Mathar_, Feb 25 2015
%o (PARI) a(n)=polcoeff((1+3*x-sqrt(1-6*x+5*x^2+x*O(x^n)))/2,n)
%Y Essentially same as A002212.
%K nonn
%O 1,1
%A _Clark Kimberling_
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