$a_n = \dbinom{n}{a_{n-1}}$ for $n>1$ , and $a_1 = 1$ .

What is $a_{64}$ ?

**
Clarification:
**
The notation
$\binom{x}{y}$
indicates "x choose y" or the
binomial coefficient
indexed by x and y.

**
Image credit:
**
http://www.fluenceportland.com/

The answer is 64.

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We claim that $a_n = n$ for all $n$ and then prove it by induction.

The claim is also true for $n+1$ , therefore it is true for all $n$ .

Therefore, $a_{64} = \boxed{64}$ .