I need to calculate
$$\sum_{k=1}^{n}\binom{k}{m_1}\binom{m_2}{k}(-1)^k$$
where $1\leq m_2 \leq m_1 \leq n$. Any help or tips on how to proceed? Thanks in advance.
2026-04-07 08:01:27.1775548887
A binomial identity question.
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Hint: $$\binom{m_2}{k}\binom{k}{m_1}=\binom{m_2}{m_1}\binom{m_2-m_1}{k-m_1}$$