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

Terms

a(0) =0a(1) =1a(2) =0a(3) =9a(4) =28a(5) =485a(6) =4866a(7) =83587a(8) =1428456a(9) =30190617a(10) =698093830a(11) =18258392471a(12) =523907661036