# Sum outta nowhere!

**Calculus**Level 5

\[\large{\displaystyle \sum_{k=1}^{\infty}\frac{(-1)^{k}k^{2}( \ln(7))^{k}}{\Gamma(k)}}\]

If the value of above summation equals \[\large{\frac{A}{B}\left(-(\ln 7)^{C}+D (\ln 7)^{E}-(\ln 7)^{F}\right)} . \]

Find the six digit number \(\overline{ABCDEF}\).

**Details And Assumptions:**

\(A,B,C,D,E,F\) are positive integers not all distinct.

\(C<E<F\)