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

Terms

a(0) =1a(1) =0a(2) =2a(3) =6a(4) =4a(5) =48a(6) =44a(7) =216a(8) =664a(9) =984a(10) =5216a(11) =9312a(12) =30160a(13) =93312a(14) =194528a(15) =717792a(16) =1674688a(17) =4842624a(18) =14554304a(19) =35517312a(20) =112151680a(21) =293213568a(22) =823387136a(23) =2409934848a(24) =6348908800a(25) =18760218624a(26) =51418362368a(27) =143838905856a(28) =414017065984