a(n) = ceiling((-1)^n*n!*(E(n,2)-E(n,1)*E(n-1,1))) where E(n,x) = Sum_{k=0..n} (-1)^k*x^k/k!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =9a(6) =15a(7) =27a(8) =48a(9) =87a(10) =160a(11) =296a(12) =552a(13) =1033a(14) =1941a(15) =3663a(16) =6936a(17) =13171a(18) =25076a(19) =47854a(20) =91515a(21) =175352a(22) =336587a(23) =647132a(24) =1246070a(25) =2402691a(26) =4638909a(27) =8967212a(28) =17353538a(29) =33618333