%I #12 Feb 04 2025 17:48:36
%S 1,0,1,0,0,1,2,4,10,24,56,133,318,760,1822,4384,10576,25578,62020,
%T 150744,367220,896496,2193104,5375405,13199606,32468912,80000438,
%U 197423104,487921440,1207578750,2992704924,7426194328,18449964876,45890849360
%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5, with initial values 1,0,1,0.
%F Conjecture: n*a(n) +2*(-2*n+3)*a(n-1) +4*(n-3)*a(n-2) +2*(-2*n+9)*a(n-3) +8*(n-6)*a(n-4)=0. - _R. J. Mathar_, May 30 2014
%F G.f.: 1/2 - sqrt(8*x^4-4*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]] = 0; aa[[3]] = 1; aa[[4]] = 0; 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 1,7
%A _Clark Kimberling_