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　次の条件で定まる数列$\{ a_n \}$の一般項を求めよ．
\[ a_1=1, \hspace{1zw} \frac{2^n}{n \, !}=\sum_{k=1}^{n+1}a_ka_{n+2-k}
\hspace{1zw} (n=1, \, 2, \, 3, \, \cdots\cdots) \]
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