递推式:
fn,k=∑i=0kfn−1,in+if_{n, k} = \sum_{i = 0}^k \frac{f_{n - 1, i}}{n + i}fn,k=∑i=0kn+ifn−1,i
边界:
f0,k=1f_{0, k} = 1f0,k=1
给定 n⩽109n \leqslant 10^9n⩽109,对于所有 1⩽k⩽2001 \leqslant k \leqslant 2001⩽k⩽200 求 fn,kf_{n, k}fn,k
/kel