a(n) = floor((-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) =8a(6) =14a(7) =26a(8) =47a(9) =86a(10) =159a(11) =295a(12) =551a(13) =1032a(14) =1940a(15) =3662a(16) =6935a(17) =13170a(18) =25075a(19) =47853a(20) =91514a(21) =175351a(22) =336586a(23) =647131a(24) =1246069a(25) =2402690a(26) =4638908a(27) =8967211a(28) =17353537a(29) =33618332