How many non-negative integers solutions are there for $x_1+2x_2+3x_3+...+nx_n=n$? (n is a non-negative integer parameter).
I can solve it with n sums one inside the other, but it isn't so nice as a final answer.
Thanks :)
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2Welcome to MSE. You'll get a lot better reaction if you post your solution, even if it isn't very nice. – saulspatz Jul 27 '19 at 17:02
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@AnuragA In the question you post there is no answer to this question. Maybe the solution is on OEIS? – Crostul Jul 27 '19 at 17:11
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@AnuragA Interestingly enough, it seems one can give an a lot better answer to this question than to the more general one (the solution is the number of partitions of $n$) – Sudix Jul 27 '19 at 17:29
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@Crostul The coefficient of $x^n$ in $\prod_{i=1}^{n} \frac{1}{1-x^{i}}$ is a perfectly reasonable answer unless you really want a closed form. In addition if you are fine with the asymptotics, as it seems the poster of AnuragA's post was, one can be adapted from here https://math.stackexchange.com/questions/32677/asymptotics-for-partitions-of-n-with-largest-part-at-most-k-or-into-at-most – parafoo Jul 27 '19 at 17:34
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Also this one – rtybase Jul 27 '19 at 17:34