a(n) = n*(n + 1)*(n^2 - n + 3)/6.

Terms

a(0) =0a(1) =1a(2) =5a(3) =18a(4) =50a(5) =115a(6) =231a(7) =420a(8) =708a(9) =1125a(10) =1705a(11) =2486a(12) =3510a(13) =4823a(14) =6475a(15) =8520a(16) =11016a(17) =14025a(18) =17613a(19) =21850a(20) =26810a(21) =32571a(22) =39215a(23) =46828a(24) =55500a(25) =65325a(26) =76401a(27) =88830a(28) =102718a(29) =118175