According to Wikipedia's article on indefinite sums, they list the following formula near the bottom of the page:
$\displaystyle \sum_x{\Gamma(x)}=(-1)^{x+1}\Gamma(x)\frac{\Gamma(1-x,-1)}{e}+C$
However, in Mathematica 7.0.1, I get the following:
$\displaystyle\sum_x{(x-1)!} = $ $\displaystyle \sum_x{\Gamma(x)} = (-1)^{x+2}\Gamma(x+1)\frac{\Gamma(1-(x+1),-1)}{e}+ (-1)^{2}\Gamma(1)\frac{\Gamma(0,-1)}{e}$
Where I've substituted $(-1)^{2}\Gamma(1)\frac{\Gamma(0,-1)}{e}$ for $C$.
Can someone please confirm that my equations are correct? I'm using this formula for an important algorithm, and I'd like to be certain that the math checks out. Thanks!