a(n) = Sum_{k=0..floor((n-1)/2)} (3^k-1)*binomial(n, 2*k+1).

Terms

a(0) =2a(1) =8a(2) =28a(3) =88a(4) =264a(5) =768a(6) =2192a(7) =6176a(8) =17248a(9) =47872a(10) =132288a(11) =364416a(12) =1001600a(13) =2748416a(14) =7532800a(15) =20627968a(16) =56452608a(17) =154423296a(18) =422276096a(19) =1154447360a(20) =3155544064a(21) =8624177152a(22) =23567831040a(23) =64400793600a(24) =175970803712a(25) =480810303488