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Coefficient of a high power of x in (1-x)^(n+1) (1+x+x^2)^n

The same question, asked 2 times: 2021 Paper 11*, 27 Jan 2024. Every wording below, oldest first.

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  1. Question 1

    2021 Paper 11

    52
    The coefficient of x256x^{256} in the expansion of (1−x)101(x2+x+1)100(1 - x)^{101}\left( x^{2}+ x + 1 \right)^{100} is:

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  2. Question 2

    27 Jan 2024

    175
    The coefficient of x2012x^{2012} in the expansion of (1−x)2008(1+x+x2)2007(1 - x)^{2008}\left( 1 + x +x^{2} \right)^{2007} is equal to