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

Terms

a(0) =1a(1) =2a(2) =3a(3) =7a(4) =21a(5) =71a(6) =253a(7) =925a(8) =3433a(9) =12871a(10) =48621a(11) =184757a(12) =705433a(13) =2704157a(14) =10400601a(15) =40116601a(16) =155117521a(17) =601080391a(18) =2333606221a(19) =9075135301a(20) =35345263801a(21) =137846528821a(22) =538257874441