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What would a explicit formula for this sequence? a_k = a_(k-1)/k? The way I find explicit formula is to write out some terms but this time it's not working.. I'd appreciate your help!

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  • $\begingroup$ So, $$a_n=\frac{a_{n-r}}{\prod_{0\le k\le r-1}(n-k)}$$ DO you have any terminating condition like $a_1,a_0$ etc.? $\endgroup$ – lab bhattacharjee Dec 20 '13 at 16:21
  • $\begingroup$ a_1=2. How did you get such a formula so quick? It looks complicated... $\endgroup$ – user48601 Dec 20 '13 at 16:22
  • $\begingroup$ And k should be k>=2, sorry I forget to state in the problem $\endgroup$ – user48601 Dec 20 '13 at 16:22
  • $\begingroup$ have you received your answer? $\endgroup$ – lab bhattacharjee Dec 20 '13 at 16:25
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$$a_k=\frac{a_{k-1}}{k}=\frac{a_{k-2}}{k(k-1)}=......=\frac{a_1}{k!}$$

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  • $\begingroup$ Thanks! The denominator is growing so fast, must the factorial! $\endgroup$ – user48601 Dec 20 '13 at 16:27

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