# Wonderfully Scary

Algebra Level 5

What is the coefficient of $$x^{101}$$ in the expansion of $\left(1-x \right)\left(1-2x\right)\left(1-2^{2}x\right) \cdots \left(1-2^{100}x\right)\left(1-2^{101}x\right) ?$

Clarification: The coefficient $$x$$ in $$1729x$$ is $$1729$$.

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