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

Terms

a(0) =1a(1) =0a(2) =2a(3) =2a(4) =4a(5) =16a(6) =12a(7) =72a(8) =88a(9) =264a(10) =608a(11) =1056a(12) =3280a(13) =5504a(14) =15328a(15) =31904a(16) =71104a(17) =175488a(18) =358080a(19) =900736a(20) =1925248a(21) =4518016a(22) =10404864a(23) =23138304a(24) =54970624a(25) =122038272a(26) =286077440a(27) =651510272a(28) =1492685824a(29) =3465687040