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%I #12 Feb 04 2025 17:24:45
%S 1,2,1,1,6,17,60,201,688,2370,8218,28703,100846,356370,1265918,
%T 4518571,16200070,58317298,210718174,764015412,2778955460,10137598506,
%U 37082361204,135985402371,499840932062,1841260760276,6796395432602,25134116857096
%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5, with initial values 1,2,1,1.
%F Conjecture: n*a(n) +2*(-2*n+3)*a(n-1) +4*(-n+3)*a(n-2) +6*(2*n-9)*a(n-3) +20*(n-6)*a(n-4)=0. - _R. J. Mathar_, Nov 21 2014
%F G.f.: 1/2 - sqrt(20*x^4+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; aa[[4]] = 1; Do[aa[[n]] = Sum[aa[[k]]*aa[[n-k]],{k,1,n-1}],{n,5,nmax}]; aa (* _Vaclav Kotesovec_, Jan 25 2015 *)
%K nonn
%O 1,2
%A _Clark Kimberling_