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

Terms

a(0) =1a(1) =2a(2) =8a(3) =51a(4) =460a(5) =5425a(6) =79206a(7) =1377985a(8) =27801096a(9) =637630353a(10) =16376303530a(11) =465451009441