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A025228 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3, with initial terms 2,1.

%I A025228 #24 Feb 07 2025 00:34:05
%S A025228 2,1,4,17,76,354,1704,8421,42508,218318,1137400,5996938,31940792,
%T A025228 171605956,928931280,5061593709,27739833228,152809506582,845646470616,
%U A025228 4699126915422,26209721959656,146681521121244,823429928805936,4635568494271458
%N A025228 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3, with initial terms 2,1.
%C A025228 Essentially A005572 shifted right twice, and 2 prepended.
%H A025228 Vincenzo Librandi, <a href="/A025228/b025228.txt">Table of n, a(n) for n = 1..200</a>
%F A025228 G.f.: (1-sqrt(1-8*x+12*x^2))/2. - _Michael Somos_, Jun 08 2000
%F A025228 n*a(n) = (8*n-12)*a(n-1) - 12*(n-3)*a(n-2). [_Richard Choulet_, Dec 16 2009]
%F A025228 a(n) ~ 6^(n-1/2)/(2*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 11 2013
%t A025228 Rest[CoefficientList[Series[(1-Sqrt[1-8x+12x^2])/2,{x,0,30}],x]]  (* _Harvey P. Dale_, Apr 20 2011 *)
%o A025228 (PARI) a(n)=polcoeff((1-sqrt(1-8*x+12*x^2+x*O(x^n)))/2,n)
%K A025228 nonn
%O A025228 1,1
%A A025228 _Clark Kimberling_
%E A025228 Name clarified by _Robert C. Lyons_, Feb 06 2025