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一些好用的结论 - He Kai's blog

一些好用的结论

$$n^k=\sum_{i=0}^{n}S(k,i)*C_n^i*i!$$

($S(k,i)$为第二类斯特林数)

 

二项式反演

$$f_n=\sum_{i=0}^{n}(-1)^i\binom{n}{i}g_i\Leftrightarrow g_n=\sum_{i=0}^{n}(-1)^i\binom{n}{i}f_i$$
$$f_n=\sum_{i=0}^{n}(-1)^i\binom{n}{i}g_i\Leftrightarrow g_n=\sum_{i=0}^{n}(-1)^{n-i}\binom{n}{i}f_i$$

莫比乌斯反演

$$f(n)=\sum_{d|n}g(d)\Leftrightarrow g(n)=\sum_{d|n}\mu(d)f(\frac{n}{d})$$

导数运算(摘自百度)

preview

 

第二类斯特林数

$$S(n,m)=\frac{1}{m!}\sum_{k=0}^{m}(-1)^k\binom{m}{k}(m-k)^n$$
$$S(n,m)=S(n-1,m-1)+m*S(n-1,m)$$

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  1. lzw说道:

    强的

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