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Question Number 206861 by MrGHK last updated on 28/Apr/24

$$\underset{\mathbf{k}=1}{\mathbf{\sum }^{\mathrm{\infty }}}\frac{1}{{\mathbf{k}}^2}\underset{\mathbf{n}=0}{\mathbf{\sum }^{\mathrm{\infty }}}\frac{1}{2^{1+\mathbf{n}}}\left(\frac{\mathbf{\Gamma }(\mathbf{n}+1)\mathbf{\Gamma }(\mathbf{k}+1){\mathbf{H}}_{\mathbf{n}+\mathbf{k}+1}}{\mathbf{\Gamma }(\mathbf{n}+\mathbf{k}+2)}\right)=???$$

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