MathDB

It is well known that the mathematical constant

e

can be written in the form

e = \tfrac{1}{0!}+\tfrac{1}{1!}+\tfrac{1}{2!}+\cdots

. With this in mind, determine the value of

\sum_{j=3}^\infty\dfrac{j}{\lfloor\frac j2\rfloor!}.

Express your answer in terms of

e

4