I was asked this by a friend. Hoping someone to answer. The goal here is to find a general formula for the expression.
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3The series grows sharply. It makes more sense to look for an asymptotic approximation rather than a general formula. – nonstudent Sep 24 '22 at 14:10
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See also this post, which has also no explicit formula. Your friend can have a look at this post. – Dietrich Burde Sep 24 '22 at 15:03
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I derived a complete asymptotic expansion here. – Gary Sep 26 '22 at 15:56
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For these problems, you can always search the OEIS with the first few terms.
https://oeis.org/search?q=1%2C28%2C3153&sort=&language=english&go=Search
You see that this sequence has been considered by others before, that there's no known exact formula (at least not there, but I have a feeling there's likely no closed formula at all), but there is an asymptotic estimate.
justt
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