a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^3 / k!.

Terms

a(0) =0a(1) =1a(2) =6a(3) =9a(4) =28a(5) =-15a(6) =306a(7) =-1799a(8) =14904a(9) =-133407a(10) =1335070a(11) =-14684439a(12) =176214996a(13) =-2290792751a(14) =32071101258a(15) =-481066515495