User:Mirceamrk/sandbox/Faulhaber's formula (→Relationship to Stirling numbers)
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Relationship to Stirling numbers[edit]
Using the unsigned Stirling numbers of the first kind and the Stirling numbers of the second kind , one can write [1]:
![{\displaystyle \left[{n \atop k}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/53e244be41a40ffd185e9edea632ba557f6ad945)
![{\displaystyle \sum \limits _{k=1}^{n}k^{p}=\sum \limits _{k=1}^{p}(-1)^{k-1}k\left[{n+1 \atop n+1-k}\right]\left\{{n+p-k \atop n}\right\}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f5dffb344c2cf589d1616fb3268579a91756431)
References[edit]
External links[edit]