# Problem #2134

 2134 Let $a_1,a_2,\cdots$, be a sequence with the following properties. (i) $a_1=1$, and (ii) $a_{2n}=n\cdot a_n$ for any positive integer $n$. What is the value of $a_{2^{100}}$? $\mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2^{99} \qquad \mathrm{(C) \ } 2^{100} \qquad \mathrm{(D) \ } 2^{4950} \qquad \mathrm{(E) \ } 2^{9999}$ This problem is copyrighted by the American Mathematics Competitions.
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