Summed Fraction Factorials

Algebra Level 5

$\frac {3}{1! + 2! + 3!} + \frac {4}{2! + 3! + 4!} + \frac {5}{3! + 4! + 5!} + \ldots + \frac {2001}{1999!+ 2000! + 2001!} = \frac {a}{b} - \frac {c}{d!}$

The equation above holds true for coprime postive integers $a$ and $b$ , and $c$ and $d$ . What is the digit sum of $(abcd)^{(abc)^{(ab)^a}}$ ?