a(n) = greatest prime < binomial(2n, n).

Terms

a(0) =5a(1) =19a(2) =67a(3) =251a(4) =919a(5) =3413a(6) =12853a(7) =48619a(8) =184753a(9) =705427a(10) =2704129a(11) =10400597a(12) =40116563a(13) =155117519a(14) =601080379a(15) =2333606183a(16) =9075135253a(17) =35345263781a(18) =137846528747a(19) =538257874423