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I've looked over this Closed form formula for $\sum\limits_{k=1}^n k^k$ but it doesn't have any explicit formula, only the bounds.

So, is it the case that no general formula can exist to calculate it or we haven't found any formula yet?

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  • $\begingroup$ This sequence grows quite rapidly - obviously larger than any particular degree of polynomial - the terms eventually exceed this degree. What makes you think a closed form exists then? It looks like any such formula would have to be exponential or larger. $\endgroup$
    – A. Thomas Yerger
    Commented Oct 5, 2016 at 5:56
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    $\begingroup$ You should search the site before posting a duplicate:math.stackexchange.com/questions/45066/… $\endgroup$
    – StubbornAtom
    Commented Oct 5, 2016 at 6:01
  • $\begingroup$ If you have looked over the other question then you should see that your actual question is also answered. $\endgroup$
    – StubbornAtom
    Commented Oct 5, 2016 at 6:16
  • $\begingroup$ @StubbornAtom What do you mean? I've looked over the link and all it states is that there is no formula to calculate this but it doesn't answer is it the case that we can never have such formula or we haven't found yet but will be in the future. $\endgroup$
    – ankit
    Commented Oct 5, 2016 at 6:23
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    $\begingroup$ Suppose that I was a famous mathematician and defined the polfosol's function as: $p(n)=\sum_{i=1}^n i^i$. Voila! here is the closed form $\endgroup$
    – polfosol
    Commented Oct 5, 2016 at 6:58

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