a(n) = Sum_{k = 1..n} (n - k + 1)^k.

Terms

a(0) =0a(1) =1a(2) =3a(3) =8a(4) =22a(5) =65a(6) =209a(7) =732a(8) =2780a(9) =11377a(10) =49863a(11) =232768a(12) =1151914a(13) =6018785a(14) =33087205a(15) =190780212a(16) =1150653920a(17) =7241710929a(18) =47454745803a(19) =323154696184