Is there a closed form?

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

#Algebra

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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`\boxed{123}`	$\boxed{123}$

Comments

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 - 4 years, 4 months ago

thanks aditya

space sizzlers - 4 years, 4 months ago

no it does not help much...please elaborate

space sizzlers - 4 years, 4 months ago

this might help

Ujjwal Mani Tripathi - 4 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$