# 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
1 year, 5 months 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 , $$\displaystyle [x^{49}] = \sum_{r=1}^{50}r(51-r) = 22100$$

- 1 year, 5 months ago

- 1 year, 5 months ago

no it does not help much...please elaborate

- 1 year, 5 months ago