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Question Number 126543 by pticantor last updated on 21/Dec/20

$$\underset{\mathit{k}=1}{\sum ^{\mathit{n}}}\underset{i=1}{\prod ^k}{i}^k=???$$

Answered by MJS_new last updated on 21/Dec/20

$$=\underset{k=1}{\sum ^n}{(k!)}^k$$$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{think}\mathrm{this}\mathrm{can}\mathrm{be}\mathrm{further}\mathrm{simplified}$$$$\mathrm{you}\mathrm{could}\mathrm{write}\mathrm{it}\mathrm{as}$$$$1!+{(2!)}^2+{(3!)}^3+...{(n!)}^n$$

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