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- #1

- Jan 17, 2013

- 1,667

HI folks , working on Stirling nums , how to prove ?

\(\displaystyle s(n,3)=\frac{1}{2}(-1)^{n-1}(n-1)!\left(H_{n-1}^2-H_{n-1}^{(2)}\right)

\)

where we define \(\displaystyle H_k^{(n)}= \sum_{m=1}^k \frac{1}{m^n}\)

I don't how to start

\(\displaystyle s(n,3)=\frac{1}{2}(-1)^{n-1}(n-1)!\left(H_{n-1}^2-H_{n-1}^{(2)}\right)

\)

where we define \(\displaystyle H_k^{(n)}= \sum_{m=1}^k \frac{1}{m^n}\)

I don't how to start

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