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

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =12a(5) =42a(6) =156a(7) =570a(8) =2124a(9) =7926a(10) =29844a(11) =112812a(12) =428712a(13) =1635108a(14) =6259236a(15) =24031260a(16) =92517180a(17) =357019224a(18) =1380671532a(19) =5349496152a(20) =20762603724a(21) =80709201504a(22) =314178212928