a(n) = binomial(composite(n), n), where composite = A002808, composite numbers.

Terms

a(0) =4a(1) =15a(2) =56a(3) =126a(4) =252a(5) =924a(6) =3432a(7) =6435a(8) =11440a(9) =43758a(10) =167960a(11) =293930a(12) =497420a(13) =1961256a(14) =3268760a(15) =5311735a(16) =8436285a(17) =13123110a(18) =54627300a(19) =225792840a(20) =354817320a(21) =548354040a(22) =834451800a(23) =1251677700a(24) =5414950296a(25) =8122425444a(26) =12033222880