cp's OEIS Frontend

A025239 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.

%I A025239 #16 Mar 02 2015 02:47:13
%S A025239 2,3,6,21,78,318,1356,5997,27222,126138,594132,2836290,13692300,
%T A025239 66729180,327855768,1622216829,8076311142,40427919714,203353800324,
%U A025239 1027318915254,5210182030308,26517609163812,135397544040744,693364054299474
%N A025239 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-2)*a(2) for n >= 3.
%H A025239 Vincenzo Librandi, <a href="/A025239/b025239.txt">Table of n, a(n) for n = 1..200</a>
%F A025239 G.f.: (1-sqrt(1-4*x-8*x^2))/2. - _Michael Somos_, Jun 08 2000
%F A025239 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 A025239 a(n) ~ sqrt(3-sqrt(3))*(2+2*sqrt(3))^n/(4*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 07 2012
%t A025239 Join[{2},Drop[CoefficientList[Series[(1-Sqrt[1-4x-8x^2])/2, {x,0,30}], x],2]] (* _Harvey P. Dale_, Nov 05 2011 *)
%o A025239 (PARI) a(n)=polcoeff((1-sqrt(1-4*x-8*x^2+x*O(x^n)))/2,n)
%Y A025239 Essentially the same as A025229.
%K A025239 nonn
%O A025239 1,1
%A A025239 _Clark Kimberling_