Your formula is correct. Taking 1-SumOf(ProbNotHappen) is the same as SumOf(ProbHappen). The former equation however uses less summations for all time when the number of outs you need is less than half of the number of remaining draws. Note that this formula will not work for multi-card straight draws or pair draws as there are other factors to consider.

Here is an app I recently made, looking for feedback...it won't let me direct link (assuming bc I am new?)
"https://play.google.com/store/apps/details?id=com.ofcprobabilitycalculator&feature=se arch_result#?t=W251bGwsMSwyLDEsImNvbS5vZmNwcm9iYWJ pbGl0eWNhbGN1bGF0b3IiXQ"