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Is there a closed form?

Can anyone help me to find the coefficient of \(x^{49}\) in \[ \displaystyle \prod_{r=1}^{50} [x - r(51-r)]? \]

Note by Space Sizzlers
6 months, 4 weeks ago

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Coefficient of \(x^{49}\) is equivalent to finding the sum of the roots of the equation if the expression is equated to zero.

In this case , \(\displaystyle [x^{49}] = \sum_{r=1}^{50}r(51-r) = 22100\) Aditya Narayan Sharma · 6 months, 4 weeks ago

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@Aditya Narayan Sharma thanks aditya Space Sizzlers · 6 months, 4 weeks ago

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no it does not help much...please elaborate Space Sizzlers · 6 months, 4 weeks ago

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this might help Starwar Clone · 6 months, 4 weeks ago

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