Show that following formula is true:
$$ \sum_{i=0}^{[n/2]}(-1)^i (n-2i)^n{n \choose i}=2^{n-1}n! $$
Using formula calculate $$ \sum_{i=0}^n(2i-n)^p{p \choose i} $$
Show that following formula is true:
$$ \sum_{i=0}^{[n/2]}(-1)^i (n-2i)^n{n \choose i}=2^{n-1}n! $$
Using formula calculate $$ \sum_{i=0}^n(2i-n)^p{p \choose i} $$