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%I #21 Jun 15 2022 11:36:59
%S 2,1,4,17,76,354,1704,8421,42508,218318,1137400,5996938,31940792,
%T 171605956,928931280,5061593709,27739833228,152809506582,845646470616,
%U 4699126915422,26209721959656,146681521121244,823429928805936,4635568494271458
%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3.
%C Essentially A005572 shifted right twice, and 2 prepended.
%H Vincenzo Librandi, <a href="/A025228/b025228.txt">Table of n, a(n) for n = 1..200</a>
%F G.f.: (1-sqrt(1-8*x+12*x^2))/2. - _Michael Somos_, Jun 08 2000
%F n*a(n) = (8*n-12)*a(n-1) - 12*(n-3)*a(n-2). [_Richard Choulet_, Dec 16 2009]
%F a(n) ~ 6^(n-1/2)/(2*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 11 2013
%t Rest[CoefficientList[Series[(1-Sqrt[1-8x+12x^2])/2,{x,0,30}],x]] (* _Harvey P. Dale_, Apr 20 2011 *)
%o (PARI) a(n)=polcoeff((1-sqrt(1-8*x+12*x^2+x*O(x^n)))/2,n)
%K nonn
%O 1,1
%A _Clark Kimberling_
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