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

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =21a(5) =65a(6) =215a(7) =713a(8) =2809a(9) =11425a(10) =49339a(11) =234825a(12) =1148013a(13) =6009153a(14) =33216239a(15) =190115849a(16) =1152491825a(17) =7244099617a(18) =47387741107a(19) =323632894729