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

Terms

a(0) =-1a(1) =0a(2) =2a(3) =12a(4) =72a(5) =520a(6) =5040a(7) =67284a(8) =1156736a(9) =23655888a(10) =549676800a(11) =14216252380a(12) =405068387328