a(n)=(1/2)*T(2n+1,n+1), where T is given by A048113.

Terms

a(0) =1a(1) =3a(2) =9a(3) =30a(4) =102a(5) =360a(6) =1290a(7) =4704a(8) =17334a(9) =64512a(10) =241836a(11) =912384a(12) =3459876a(13) =13178988a(14) =50389236a(15) =193295652a(16) =743610528a(17) =2867892588a(18) =11085281328a(19) =42933166380a(20) =166575534264a(21) =647329281456