E.g.f.: 1/Product_{k>0} (1+x^k/k!)^k.

Terms

a(0) =1a(1) =-1a(2) =0a(3) =-3a(4) =26a(5) =-75a(6) =324a(7) =-3535a(8) =30988a(9) =-242025a(10) =2245820a(11) =-26847381a(12) =339741984a(13) =-4205748547a(14) =57094691822a(15) =-883946426805