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

Terms

a(0) =1a(1) =3a(2) =7a(3) =17a(4) =45a(5) =131a(6) =419a(7) =1465a(8) =5561a(9) =22755a(10) =99727a(11) =465537a(12) =2303829a(13) =12037571a(14) =66174411a(15) =381560425a(16) =2301307841a(17) =14483421859a(18) =94909491607a(19) =646309392369