a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(4*k,n-2*k).

Terms

a(0) =1a(1) =0a(2) =2a(3) =12a(4) =30a(5) =100a(6) =446a(7) =1596a(8) =5726a(9) =22512a(10) =86112a(11) =325160a(12) =1255650a(13) =4857996a(14) =18728138a(15) =72584512a(16) =282194238a(17) =1097448192a(18) =4275805388a(19) =16690807944a(20) =65220896440a(21) =255142508976a(22) =999300655080