A Multinomial Conundrum

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sowmitra
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A Multinomial Conundrum

Unread post by sowmitra » Thu Aug 16, 2012 2:54 pm

A polynomial in $x$ is defined by
$$a_0+a_1x+a_2x^2+...+a_{2n}x^{2n}=(x+2x^2+3x^3+...+nx^n)^2$$
Show that,
\[\displaystyle\sum_{i=n+1}^{2n}a_i=\frac{n(n+1)(5n^2+5n+2)}{24}\]
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