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

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =26a(5) =77a(6) =246a(7) =805a(8) =2702a(9) =9238a(10) =32066a(11) =112674a(12) =400024a(13) =1432736a(14) =5170584a(15) =18783763a(16) =68635478a(17) =252087092a(18) =930138522a(19) =3446163221a(20) =12815663678a(21) =47820430994a(22) =178987624514a(23) =671825076732