Today, we had a math class, where we had to show, that a100>14 for
a0=1;an+1=an+a−1n
Apart from this task, I asked myself: Is there a closed form for this sequence? Since I didn't find an answer by myself, can somebody tell me, whether such a closed form exists, and if yes what it is?
Answer
I agree, a closed form is very unlikely.
As for more precise asymptotics, I think an=√2n+1/8√2ln(n)√n−1128√2(ln(n)−2)2+o(1)n3/2
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