a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027113.

Terms

a(0) =1a(1) =3a(2) =11a(3) =46a(4) =180a(5) =707a(6) =2729a(7) =10377a(8) =39045a(9) =145493a(10) =537749a(11) =1973915a(12) =7202499a(13) =26144901a(14) =94475783a(15) =340028026a(16) =1219451204a(17) =4359473611a(18) =15540448583a(19) =55255188413a(20) =196004642045a(21) =693798921723