E.g.f. (1+x^2-2x^3+x^4)/(1-x)^2.

Terms

a(0) =1a(1) =2a(2) =8a(3) =24a(4) =120a(5) =720a(6) =5040a(7) =40320a(8) =362880a(9) =3628800a(10) =39916800a(11) =479001600a(12) =6227020800a(13) =87178291200