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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4.
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%I #11 Feb 25 2015 15:07:02

%S 1,1,2,2,4,10,22,52,130,326,832,2162,5674,15032,40178,108154,292956,

%T 797994,2184430,6006028,16579138,45929838,127656504,355863330,

%U 994735442,2787537904,7829586914,22038759218,62158281844,175636481738,497142172806,1409444977380

%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4.

%F G.f.: (1 + x + x^2 - sqrt(1 - 2*x - x^2 - 6*x^3 + x^4))/2. - _Michael Somos_, Jun 08 2000

%F Conjecture: n*a(n) +(-2*n+3)*a(n-1) +(-n+3)*a(n-2) +3*(-2*n+9)*a(n-3) +(n-6)*a(n-4)=0. - _R. J. Mathar_, Feb 25 2015

%o (PARI) a(n)=polcoeff((x+x^2-sqrt(1-2*x-x^2-6*x^3+x^4+x*O(x^n)))/2,n)

%K nonn

%O 1,3

%A _Clark Kimberling_