a(n) = T(2n,n), where T is given by A048113.

Terms

a(0) =1a(1) =2a(2) =4a(3) =12a(4) =36a(5) =120a(6) =408a(7) =1440a(8) =5160a(9) =18816a(10) =69336a(11) =258048a(12) =967344a(13) =3649536a(14) =13839504a(15) =52715952a(16) =201556944a(17) =773182608a(18) =2974442112a(19) =11471570352a(20) =44341125312a(21) =171732665520a(22) =666302137056