a(n) = n! * Laguerre(n,-5).

Terms

a(0) =1a(1) =6a(2) =47a(3) =446a(4) =4929a(5) =61870a(6) =866695a(7) =13373190a(8) =224995745a(9) =4094022230a(10) =80031878175