a(n) = n*(2*n^2 -3*n +7)/6 = C(n, 1) + C(n, 2) + 2*C(n, 3).

Terms

a(0) =1a(1) =3a(2) =8a(3) =18a(4) =35a(5) =61a(6) =98a(7) =148a(8) =213a(9) =295a(10) =396a(11) =518a(12) =663a(13) =833a(14) =1030a(15) =1256a(16) =1513a(17) =1803a(18) =2128a(19) =2490a(20) =2891a(21) =3333a(22) =3818a(23) =4348a(24) =4925a(25) =5551a(26) =6228a(27) =6958a(28) =7743a(29) =8585