a(n) = binomial(2*n,n)*(n+2)^2/(n+1).

Terms

a(0) =4a(1) =9a(2) =32a(3) =125a(4) =504a(5) =2058a(6) =8448a(7) =34749a(8) =143000a(9) =588302a(10) =2418624a(11) =9934834a(12) =40770352a(13) =167152500a(14) =684656640a(15) =2801810205a(16) =11455885080a(17) =46801769190a(18) =191055480000a(19) =779363066790