a(n) = 6*(n+1)*(2*n+6)!/((n+3)!*(n+5)!).

Terms

a(0) =0a(1) =6a(2) =28a(3) =108a(4) =396a(5) =1430a(6) =5148a(7) =18564a(8) =67184a(9) =244188a(10) =891480a(11) =3268760a(12) =12034980a(13) =44482230a(14) =165002460a(15) =614106900a(16) =2292665760a(17) =8583849780a(18) =32223863880a(19) =121267584360a(20) =457412818200