E.g.f.: -1/(1-LambertW(-x))^2.

Terms

a(0) =-1a(1) =2a(2) =-2a(3) =6a(4) =8a(5) =170a(6) =1872a(7) =29246a(8) =519808a(9) =10698642a(10) =248787200a(11) =6458737142a(12) =185138721792