a(n) = 2^n*binomial((n + 1 + (n mod 2))/2, 1/2).

Terms

a(0) =1a(1) =3a(2) =6a(3) =15a(4) =30a(5) =70a(6) =140a(7) =315a(8) =630a(9) =1386a(10) =2772a(11) =6006a(12) =12012a(13) =25740a(14) =51480a(15) =109395a(16) =218790a(17) =461890a(18) =923780a(19) =1939938a(20) =3879876a(21) =8112468a(22) =16224936a(23) =33801950a(24) =67603900a(25) =140408100a(26) =280816200a(27) =581690700a(28) =1163381400a(29) =2404321560