a(n) = binomial(floor((3n+4)/2),floor(n/2)).

Terms

a(0) =1a(1) =1a(2) =5a(3) =6a(4) =28a(5) =36a(6) =165a(7) =220a(8) =1001a(9) =1365a(10) =6188a(11) =8568a(12) =38760a(13) =54264a(14) =245157a(15) =346104a(16) =1562275a(17) =2220075a(18) =10015005a(19) =14307150a(20) =64512240a(21) =92561040a(22) =417225900a(23) =600805296a(24) =2707475148a(25) =3910797436a(26) =17620076360a(27) =25518731280a(28) =114955808528a(29) =166871334960