a(n) = Sum_{k=0..n} (n-k+1)^k.

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =23a(5) =66a(6) =210a(7) =733a(8) =2781a(9) =11378a(10) =49864a(11) =232769a(12) =1151915a(13) =6018786a(14) =33087206a(15) =190780213a(16) =1150653921a(17) =7241710930a(18) =47454745804a(19) =323154696185