a(n) = binomial(floor((3n+2)/2), floor(n/2)).

Terms

a(0) =1a(1) =1a(2) =4a(3) =5a(4) =21a(5) =28a(6) =120a(7) =165a(8) =715a(9) =1001a(10) =4368a(11) =6188a(12) =27132a(13) =38760a(14) =170544a(15) =245157a(16) =1081575a(17) =1562275a(18) =6906900a(19) =10015005a(20) =44352165a(21) =64512240a(22) =286097760a(23) =417225900a(24) =1852482996a(25) =2707475148a(26) =12033222880a(27) =17620076360a(28) =78378960360a(29) =114955808528