I just came up with the sequence where a term is defined as the sum of its last predecessor with the average of all predecessors.$$a_{n+1} = a_{n} + \frac{a_1 + a_2 + ... + a_n}{n}\\$$When $a_1 = 1$, it goes like this:$$1, 2, 7/2, 17/3, ...$$
What is this sequence? What is the asymptotic order for this sequence?