Question Number 157958 by HongKing last updated on 30/Oct/21
$$\mathrm{Find}: \\ $$$$\Omega_{\boldsymbol{\mathrm{n}}} =\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n}}\left(\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\frac{\mathrm{k}^{\mathrm{3}} \:+\:\mathrm{k}^{\mathrm{2}} \:-\:\mathrm{3k}\:-\:\mathrm{2}}{\left(\mathrm{k}\:+\:\mathrm{2}\right)!}\right) \\ $$$$ \\ $$