E.g.f.: -1/((1-LambertW(-x))*(1+x)).

Terms

a(0) =-1a(1) =2a(2) =-4a(3) =15a(4) =-44a(5) =385a(6) =-294a(7) =32473a(8) =280120a(9) =8528049a(10) =170757910a(11) =4748977321a(12) =132530188308