a(n) = (n+1)^2*(n+2)^3*(n+3)/24.

Terms

a(0) =1a(1) =18a(2) =120a(3) =500a(4) =1575a(5) =4116a(6) =9408a(7) =19440a(8) =37125a(9) =66550a(10) =113256a(11) =184548a(12) =289835a(13) =441000a(14) =652800a(15) =943296a(16) =1334313a(17) =1851930a(18) =2527000a(19) =3395700a(20) =4500111a(21) =5888828a(22) =7617600a(23) =9750000a(24) =12358125a(25) =15523326a(26) =19336968a(27) =23901220a(28) =29329875a(29) =35749200