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

Terms

a(0) =1a(1) =0a(2) =2a(3) =6a(4) =4a(5) =40a(6) =28a(7) =168a(8) =296a(9) =632a(10) =2048a(11) =3104a(12) =10768a(13) =19776a(14) =51168a(15) =123616a(16) =257344a(17) =693760a(18) =1434304a(19) =3640192a(20) =8267136a(21) =19087232a(22) =46412800a(23) =103556096a(24) =252315904a(25) =575102976a(26) =1357466112a(27) =3190404608a(28) =7363810304a(29) =17495373824