A025254 - OEIS

%I #9 Jan 16 2025 11:15:25

%S 3,1,1,3,10,34,118,417,1497,5448,20063,74649,280252,1060439,4040413,

%T 15488981,59701236,231236830,899559100,3513314664,13770811198,

%U 54152480421,213585706927,844723104691,3349274471386,13310603555085,53012829376985

%N a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 3, 1, 1, 3.

%F G.f.: (1 + 3*x + x^2 - sqrt(x^4 + 2*x^3 + 7*x^2 - 6*x + 1))/(2*x). - _Vaclav Kotesovec_, Mar 02 2014

%F Recurrence: (n+1)*a(n) = 3*(2*n-1)*a(n-1) - 7*(n-2)*a(n-2) - (2*n-7)*a(n-3) - (n-5)*a(n-4). - _Vaclav Kotesovec_, Mar 02 2014

%t CoefficientList[Series[(1+3*x+x^2-Sqrt[x^4+2*x^3+7*x^2-6*x+1])/(2*x),{x,0,20}],x] (* _Vaclav Kotesovec_, Mar 02 2014 *)

%Y Cf. A178578.

%K nonn

%O 1,1

%A _Clark Kimberling_