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

Terms

a(0) =1a(1) =0a(2) =0a(3) =4a(4) =12a(5) =0a(6) =12a(7) =216a(8) =108a(9) =32a(10) =1440a(11) =4320a(12) =944a(13) =6720a(14) =50400a(15) =60672a(16) =32400a(17) =362880a(18) =1089088a(19) =788544a(20) =2042496a(21) =11177728a(22) =18242112a(23) =16410240a(24) =83355840a(25) =249910272a(26) =286820352a(27) =566097920a(28) =2406440448a(29) =4624459776