Wonderfully Scary

Algebra Level 5

What is the coefficient of x101x^{101} in the expansion of (1x)(12x)(122x)(12100x)(12101x)?\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 xx in 1729x1729x is 17291729.

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