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

Terms

a(0) =1a(1) =0a(2) =2a(3) =2a(4) =4a(5) =24a(6) =12a(7) =120a(8) =136a(9) =456a(10) =1152a(11) =1888a(12) =6800a(13) =10944a(14) =33248a(15) =70816a(16) =160064a(17) =419328a(18) =850880a(19) =2256512a(20) =4874112a(21) =11749504a(22) =27833344a(23) =62598144a(24) =153483520a(25) =344694784a(26) =827492864a(27) =1917989376a(28) =4464268288a(29) =10580625408