%I #8 Jan 25 2015 16:32:05
%S 1,-1,1,1,0,-1,0,3,4,0,-2,11,34,36,14,55,250,484,526,672,2024,5106,
%T 8388,11415,21806,53222,107954,176392,295988,615242,1316100,2462955,
%U 4271142,8015318,16478474,32815776,60660164,111589258,218042964,436588372
%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.
%F Conjecture: n*(n^4+n^3+n^2+n+1)*a(n) +(n^5+n^4+n^3+n^2+n+5)*a(n-1) +(n^5+n^4+n^3+n^2+n-52)*a(n-2) +12*(-2*n^5+5*n^4+3*n^3+2*n^2+3*n+24)*a(n-3) +2*(26*n^5-103*n^4-58*n^3-37*n^2-64*n-371)*a(n-4) +2*(-58*n^5+329*n^4+209*n^3+143*n^2+185*n+713)*a(n-5) +8*(n-8)*(13*n^4+9*n^3+7*n^2+9*n+19)*a(n-6)=0. - _R. J. Mathar_, Jan 25 2015
%F G.f.: 1/2 - sqrt(8*x^4-12*x^3+8*x^2-4*x+1)/2. - _Vaclav Kotesovec_, Jan 25 2015
%F Recurrence: n*a(n) = 2*(2*n-3)*a(n-1) - 8*(n-3)*a(n-2) + 6*(2*n-9)*a(n-3) - 8*(n-6)*a(n-4). - _Vaclav Kotesovec_, Jan 25 2015
%t nmax = 30; aa = ConstantArray[0,nmax]; aa[[1]] = 1; aa[[2]] = -1; 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 sign
%O 1,8
%A _Clark Kimberling_