# Part 3

Discrete Mathematics Level pending

Calculate $\large M=\sum \frac{1}{k_{1}!k_{2}!...k_{2016}!(k_{2}+2k_{3}+3k_{4}+...+2015k_{2016})!}$ where the sum is taken over all 2016-upples of natural numbers$\large (k_{1},k_{2},k_{3}....,k_{2016})$ satisfying $\large k_{1}+2k_{2}+3k_{3}+...+2016k_{2016}=2016$ If the answer is $\frac{a}{b}\times \begin{pmatrix} c+d &\\ e & \end{pmatrix}$ Type $$S=a+b$$

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