A025263 - OEIS

%I #15 Feb 05 2025 22:29:46

%S 1,2,1,6,16,57,190,676,2418,8860,32848,123413,468246,1792700,6915438,

%T 26856116,104908160,411944698,1625120364,6437911432,25600033700,

%U 102145852536,408840420704,1641061732941,6604395207782,26643368509676

%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4, with initial terms 1,2,1.

%F Recurrence: n*a(n) = 2*(2*n-3)*a(n-1) + 4*(n-3)*a(n-2) - 6*(2*n-9)*a(n-3). - _Vaclav Kotesovec_, Jan 25 2015

%F G.f.: 1/2 - sqrt(12*x^3-4*x^2-4*x+1)/2. - _Vaclav Kotesovec_, Jan 25 2015

%t nmax = 30; aa = ConstantArray[0,nmax]; aa[[1]] = 1; aa[[2]] = 2; aa[[3]] = 1; Do[aa[[n]]=Sum[aa[[k]]*aa[[n-k]],{k,1,n-1}],{n,4,nmax}]; aa (* _Vaclav Kotesovec_, Jan 25 2015 *)

%t CoefficientList[Series[1/2-Sqrt[12x^3-4x^2-4x+1]/2,{x,0,50}],x] (* _Harvey P. Dale_, Jan 01 2022 *)

%K nonn

%O 1,2

%A _Clark Kimberling_