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

Terms

a(0) =1a(1) =-1a(2) =-2a(3) =3a(4) =14a(5) =45a(6) =-156a(7) =-1225a(8) =-3396a(9) =-105a(10) =226760a(11) =1175229a(12) =4084200a(13) =-35683219a(14) =-585896962a(15) =-3512021955a(16) =-14398868176a(17) =198247498911