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Notes

第八章 特殊计数序列

Catalan 数

Cn=1n+1(2nn)\displaystyle{ C _{ n } = \frac{ 1 }{ n + 1 } { 2 n \choose n } }

差分序列和 Stirling 数

Δhn=hn+1−hnΔ2hn=Δ(Δhn)=Δhn+1−Δhn=hn+2−2hn+1+hn\displaystyle{ \begin{aligned}\Delta h _{ n } & = h _{ n + 1 } - h _{ n } \\ \Delta ^{ 2 } h _{ n } & = \Delta \left( \Delta h _{ n } \right) = \Delta h _{ n + 1 } - \Delta h _{ n } = h _{ n + 2 } - 2 h _{ n + 1 } + h _{ n }\end{aligned} }