O.g.f.:G(G(x)-1)where G(x)=Sum_k>=0,k!*x^k.

Terms

a(0) =1a(1) =1a(2) =4a(3) =20a(4) =116a(5) =756a(6) =5448a(7) =43032a(8) =370704a(9) =3472656a(10) =35303424a(11) =388786176a(12) =4628774016a(13) =59431077504a(14) =820503839232