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

Terms

a(0) =1a(1) =1a(2) =5a(3) =9a(4) =25a(5) =65a(6) =205a(7) =713a(8) =2753a(9) =11425a(10) =50389a(11) =234825a(12) =1155817a(13) =6009153a(14) =32958173a(15) =190115849a(16) =1148816017a(17) =7244099617a(18) =47521750501a(19) =323632894729