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If \( a_{0}, a_{1}, a_{2}, \ldots \). be the coefficients in the expansion of \( \left(1+x+x^{2}\right)^{n} \) in ascending powers of \( x \), then prove
\( \mathrm{P} \) that :

W
\[
a_{0} a_{2}-a_{1} a_{3}+a_{2} a_{4}-\ldots . .+a_{2 n-2} a_{2 n}=a_{n+1}
\]
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