a(n) = 5^n*(n^3 - 3*n^2 + 2*n + 750)/750.

Terms

a(0) =1a(1) =5a(2) =25a(3) =126a(4) =645a(5) =3375a(6) =18125a(7) =100000a(8) =565625a(9) =3265625a(10) =19140625a(11) =113281250a(12) =673828125a(13) =4013671875a(14) =23876953125a(15) =141601562500a(16) =836181640625