a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+1,2*n-6*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =6a(5) =0a(6) =4a(7) =40a(8) =20a(9) =8a(10) =168a(11) =280a(12) =72a(13) =576a(14) =2016a(15) =1376a(16) =1904a(17) =10560a(18) =14848a(19) =10272a(20) =46112a(21) =109952a(22) =95808a(23) =193024a(24) =641728a(25) =858496a(26) =993664a(27) =3227008a(28) =6312832a(29) =6963200