a(n) = (n+1)(n+2)(n+3)(35n^3 + 153n^2 + 232n + 120)/720.

Terms

a(0) =1a(1) =18a(2) =123a(3) =523a(4) =1673a(5) =4424a(6) =10206a(7) =21246a(8) =40821a(9) =73546a(10) =125697a(11) =205569a(12) =323869a(13) =494144a(14) =733244a(15) =1061820a(16) =1504857a(17) =2092242a(18) =2859367a(19) =3847767a(20) =5105793a(21) =6689320a(22) =8662490a(23) =11098490a(24) =14080365a(25) =17701866a(26) =22068333a(27) =27297613a(28) =33521013a(29) =40884288