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

Terms

a(0) =0a(1) =1a(2) =2a(3) =13a(4) =112a(5) =1321a(6) =19296a(7) =335637a(8) =6764864a(9) =154946449a(10) =3973820800a(11) =112789880413