a(n) = Sum_{k=1..n} (k+2)!/k! = Sum_{k=1..n} (k+2)*(k+1).

Terms

a(0) =0a(1) =6a(2) =18a(3) =38a(4) =68a(5) =110a(6) =166a(7) =238a(8) =328a(9) =438a(10) =570a(11) =726a(12) =908a(13) =1118a(14) =1358a(15) =1630a(16) =1936a(17) =2278a(18) =2658a(19) =3078a(20) =3540a(21) =4046a(22) =4598a(23) =5198a(24) =5848a(25) =6550a(26) =7306a(27) =8118a(28) =8988a(29) =9918