The Chudnovsky Formula for calculating $\pi$ reads:
$$\frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (545140134k + 13591409)}{(3k)!(k!)^3 640320^{3k + 3/2}}$$
If you double the second coefficient, you obtain
$$2\cdot13591409=27182818$$
which is the first 8 digits of Euler's number.
Any ideas on why this happens? Or is it just coincidence?