Catalan numbers halved and rounded to the next integer.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =7a(5) =21a(6) =66a(7) =215a(8) =715a(9) =2431a(10) =8398a(11) =29393a(12) =104006a(13) =371450a(14) =1337220a(15) =4847423a(16) =17678835a(17) =64822395a(18) =238819350a(19) =883631595a(20) =3282060210a(21) =12233133510a(22) =45741281820a(23) =171529806825a(24) =644952073662