a(n) = (n/2)*binomial(2*n, n) + 1.

Terms

a(0) =1a(1) =2a(2) =7a(3) =31a(4) =141a(5) =631a(6) =2773a(7) =12013a(8) =51481a(9) =218791a(10) =923781a(11) =3879877a(12) =16224937a(13) =67603901a(14) =280816201a(15) =1163381401a(16) =4808643121a(17) =19835652871a(18) =81676217701a(19) =335780006101