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

Terms

a(0) =1a(1) =2a(2) =7a(3) =24a(4) =79a(5) =258a(6) =851a(7) =2852a(8) =9715a(9) =33582a(10) =117561a(11) =416012a(12) =1485787a(13) =5348866a(14) =19389675a(15) =70715324a(16) =259289563a(17) =955277382a(18) =3534526361a(19) =13128240820a(20) =48932534019a(21) =182965127258a(22) =686119227277