n^n - (-1)^n (n-1)^(n-1).
2, 3, 31, 229, 3381, 43531, 870199, 15953673, 404197705, 9612579511, 295311670611, 8630788777645, 311791207040509, 10809131718965763, 449005897206417391, 18008850183328692241, 845687005960046315793, 38519167813410200811247
1
This sequence definition has a minus sign instead of a plus sign after the n^n term that S000989 has.
T. D. Noe, Plot of 300 terms
T. D. Noe, Table of 300 terms
(Mma) Table[n^n - (-1)^n (n - 1)^(n - 1), {n, 20}]
Cf. S000989.
nonn
T. D. Noe, Mar 21 2017