159) $a_n = \sum_{k=0}^{n} (-1)^k \binom{n}{k} (n-k+1)^n$
Now, let's plug in $n=2$:
$a_2 = \sum_{k=0}^{2} (-1)^k \binom{2}{k} (2-k+1)^2$
Now, let's expand the sum:
$a_2 = (-1)^0 \binom{2}{0} (2-0+1)^2 + (-1)^1 \binom{2}{1} (2-1+1)^2 + (-1)^2 \binom{2}{2}
Show more…