Doubt from Summation

Require help
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Sorry
The upper Summation has upper limit till 'r'

Coefficient of x^{2r} in \displaystyle (1+x+x^2)^{n}

Coeff. of \displaystyle x^{2r} in

\bigg[1+x(1+x)\bigg]^{n}=\displaystyle \sum^{n}_{k=0}\binom{n}{2k}\binom{n-2k}{r-k}.

Coeff. of \displaystyle x^{2r} in

\bigg[\bigg(x+\frac{1}{2}\bigg)^2+\frac{3}{4}\bigg]^{n}=\displaystyle \sum^{n}_{k=0}\binom{n}{k}\bigg(\frac{3}{4}\bigg)^{n-k}\bigg(\frac{1}{2}\bigg)^{2k-2r}.

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