a(n) = T(2*n+2,n), array T as in A055216.

Terms

a(0) =1a(1) =4a(2) =15a(3) =51a(4) =168a(5) =540a(6) =1711a(7) =5365a(8) =16698a(9) =51679a(10) =159250a(11) =489048a(12) =1497681a(13) =4576140a(14) =13955895a(15) =42493677a(16) =129211818a(17) =392441049a(18) =1190716836a(19) =3609608838a(20) =10933915743a(21) =33097421223a(22) =100126350090a(23) =302737691646a(24) =914897836063