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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 #16 Mar 02 2015 02:47:13

%S 2,3,6,21,78,318,1356,5997,27222,126138,594132,2836290,13692300,

%T 66729180,327855768,1622216829,8076311142,40427919714,203353800324,

%U 1027318915254,5210182030308,26517609163812,135397544040744,693364054299474

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

%H Vincenzo Librandi, <a href="/A025239/b025239.txt">Table of n, a(n) for n = 1..200</a>

%F G.f.: (1-sqrt(1-4*x-8*x^2))/2. - _Michael Somos_, Jun 08 2000

%F Recurrence (for n>3): n*a(n) = 2*(2*n-3)*a(n-1) + 8*(n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 07 2012

%F a(n) ~ sqrt(3-sqrt(3))*(2+2*sqrt(3))^n/(4*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 07 2012

%t Join[{2},Drop[CoefficientList[Series[(1-Sqrt[1-4x-8x^2])/2, {x,0,30}], x],2]] (* _Harvey P. Dale_, Nov 05 2011 *)

%o (PARI) a(n)=polcoeff((1-sqrt(1-4*x-8*x^2+x*O(x^n)))/2,n)

%Y Essentially the same as A025229.

%K nonn

%O 1,1

%A _Clark Kimberling_