a(n) = Sum_{k=1..n} ceiling(k^n/n^k).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =8a(5) =15a(6) =27a(7) =57a(8) =142a(9) =381a(10) =1110a(11) =3484a(12) =11678a(13) =41566a(14) =156319a(15) =618829a(16) =2570651a(17) =11174315a(18) =50704149a(19) =239641306a(20) =1177394450a(21) =6002778135a(22) =31706648191a(23) =173250478087a(24) =977993291266