## 413_difference Sequence

⚠️THIS NOTE IS NOT FINISHED YET TODO: stirling number definitions stirling number of the first and the second type bell number Question Can you find a closed formula for the sum of the $p$-th powers of the first $n$ positive integers? That is, we need a closed formulat for the sequence: $$ h_n=a_p n^p+a_{p-1} n^{p-1}+\cdots+a_1 n+a_0, \quad(n \geq 0) $$ Solution The method is to use difference sequences. We already know the following:...