a(n) = Sum_{k >= 0} floor(n^k / k!).

Terms

a(0) =1a(1) =2a(2) =6a(3) =18a(4) =50a(5) =143a(6) =397a(7) =1088a(8) =2973a(9) =8093a(10) =22014a(11) =59861a(12) =162742a(13) =442396a(14) =1202589a(15) =3268996a(16) =8886090a(17) =24154933a(18) =65659949a(19) =178482278a(20) =485165168a(21) =1318815708a(22) =3584912818a(23) =9744803414a(24) =26489122097a(25) =72004899306a(26) =195729609397a(27) =532048240570