题意
[sum_{i=0}^{n}inom{n}{i}(i^k-(n-i)^k)^2 ]
做法
[egin{aligned}
sumlimits_{i=0}^{n}inom{n}{i}(i^k-(n-i)^k)^2&=sumlimits_{b=0}^{m-1}{n\%mchoose b}sumlimits_{a=0}^{frac{n-b}{m}}{nchoose am+b}(b^k-(n-b)^k)^2\
&=sumlimits_{b=0}^{min(m-1,n\%m)}{n\%mchoose b}sumlimits_{a=0}^{frac{n-b}{m}}{nchoose am+b}(b^k-(n-b)^k)^2\
&=sumlimits_{a=0}^{frac{n}{m}}{frac{n}{m}choose a}sumlimits_{b=0}^{n\%m}{n}{n\%m choose b}(b^k-(n-b)^k)\
end{aligned}]