Find the coefficient of $x^{49}$ in the expansion of
\[(x + 1)(x + 3)(x + 5) \dotsm (x + 95)(x + 97)(x + 99).\]
Question:
Find the coefficient of $x^{49}$ in the expansion of
\[(x + 1)(x + 3)(x + 5) \dotsm (x + 95)(x + 97)(x + 99).\]
Answer:
Let's think step by step.

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Find the coefficient of $x^{49}$ in the expansion of
\[(x + 1)(x + 3)(x + 5) \dotsm (x + 95)(x + 97)(x + 99).\]
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