a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(2*k+2,2*n-4*k+1).

Terms

a(0) =1a(1) =0a(2) =4a(3) =8a(4) =12a(5) =80a(6) =80a(7) =448a(8) =976a(9) =2176a(10) =8256a(11) =14720a(12) =52416a(13) =124672a(14) =313600a(15) =956416a(16) =2145536a(17) =6438912a(18) =16135168a(19) =42117120a(20) =117754880a(21) =290820096a(22) =812109824a(23) =2091991040a(24) =5519691776a(25) =14911766528a(26) =38335299584a(27) =103777271808a(28) =271034662912a(29) =716987629568